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It’s opening day of Paul Thomas Anderson’s “One Battle After Another,” and Alejandro González Iñárritu is worried about how it will play with audiences. “I just cross my fingers that people go in millions,” he told me. “I hope, because it’s so important.”

We are talking on Zoom, and of course, Iñárritu is rooting for PTA: He’s a fellow auteur who makes expensive original movies with movie stars. (BTW, the $130-million movie opened to $22 million.) For his part, Iñárritu just wrapped principal photography in April on an untitled comedy ensemble led by Tom Cruise and produced by Legendary for Warner Bros.

The Mexican filmmaker is directing his first English-language movie since 2015’s “The Revenant,” which won “One Battle After Another” star Leonardo DiCaprio his first Oscar. The untitled Cruise comedy, shot in 35-millimeter VistaVision by three-time Oscar-winner Emmanuel “Chivo” Lubezki, should come out sometime next fall. The director is in the editing room.

“We’re going to finish in February, March,” he said. “We still have a long way [in] post-production.”

Even though both Iñárritu and Cruise are powerful, controlling perfectionists on a movie production, “it was the most amazing, unexpected, sweet, gentle relation that I have had on a set,” Iñárritu said. “His manners, his understanding, his passion, and his integrity, and the way he prepares. He loves the process. Filmmaking has been his life for 40 years. I have never seen somebody so devoted. I was happy to share with him that passion. And at the same time, we built an incredible relation of mutual trust. He will surprise the world. People will see a new kind of thing. It was blessed, and not only him, but all the cast: Riz Ahmed, Sandra Hüller, John Goodman, and Jesse Plemons. We had a blast. It was challenging, but it was wild comedy. And we laugh a lot. We have a wild time.”

But we are not Zooming to talk about Cruise. This May, to celebrate the 25th anniversary of “Amores Perros,” Iñárritu’s daring triptych debut feature, shot in Mexico City and introducing Gael García Bernal, the director screened the restored 4K version at Cannes to a packed house. The movie holds up: It’s vivid, loud, assaultive, and violent, from the visceral dogfights (no animals were harmed) to the glam model (Goya Toledo) who is forever mutilated in a car crash. A brand-new 5.1 surround sound mix by Jon Taylor at NBCUniversal StudioPost enhances the intensity.

The director hesitated to watch the film at the Cannes Classics showing. He had undergone the painstaking Criterion restoration for the 20th anniversary in 2020 with cinematographer Rodrigo Prieto, but had only watched the film in bits and pieces.

“I hadn’t seen the film complete in 25 years,” he said. “The film was shot in a bleach-bypass process, or silver retain, which is a very corrosive thing, because the silver stays in the negative. So we have to restore a lot of things. [I thought] what young man did that? And all the effort that it took for all of us who did the film, the amount of work, considering the little money we have, and so little time. What I can tell you is that I was impressed by the muscle. It hasn’t become a flaccid film.”

“Amores Perros” played Cannes 25 years ago, but not in Competition, where it was roundly rejected before it went to the selection committee. Luckily, it was invited to Critics’ Week, won the Grand Prix, and landed a North American release in 2001 from Lionsgate. The rest is history. It launched the careers of Iñárritu, 19-year-old García Bernal, and Prieto, among others. After the screening, a grateful and teary García Bernal said, “It’s a film that we all were transformed, and even the way in Mexico we were perceived, the films were transformed.”

“Even when we were a very small independent film in a very small section that is not even official, it became the film that everybody wanted to see,” said Iñárritu. The film was nominated for the Best Foreign Language Film Oscar; the writer, director, and producer went on to win Best Director for “Birdman” and “The Revenant,” and Original Screenplay and Best Picture (“Birdman”).

When they made “Amores Perros,” the filmmaker explained, the Mexican film industry was producing only five to seven local films a year from the same few directors, with a nationalistic flavor, subsidized by the government. Maybe one would wind up in theaters. “Every director that I knew at that time, they [had] just made one film,” he said. “And they were already 50 years old. A film was considered a one-time opportunity, and you better make sure that you put all you have to say there.”

Also based in Mexico City, novelist Guillermo Arriaga wrote the screenplay for “Amores Perros,” “an incredible, solid, complex script,” said Iñárritu. “Mexico City is a complex city with incredible ancient culture with visual traditions. It has the third most museums in the world. And we were middle-class, educated. So we can see and observe: low, high, wherever. We were having access to many things.”

The “Amores Perros” team had been working together making commercials and videos for seven years. They were already quite sophisticated. “We were all Chilango, so we knew exactly how that city smells and feels,” said Iñárritu. “There was a new government coming, that threw out the party dictatorship of 70 years. So there was hope and a feeling that we need[ed] to shake who we were, how we talk about ourselves, how we see ourselves. This film came into the right moment.”

Iñárritu has written an essay about making the film for Mack Books’ just-published “Amores Perros” book, which also showcases unseen set photography, critical essays, and production documents. And “Sueño Perro: Alejandro G. Iñárritu’s Celluloid Installation” is making the rounds, starting at Fondazione Prada in Milan and LagoAlgo in Mexico City, and then moving in February to LACMA in Los Angeles.

Back in 2020, “Amores Perros,” which runs two hours and 37 minutes, was edited down from 1 million feet of material. “That means 15,000 feet of film of 35 millimeters,” said Iñárritu, “so 985,000 feet were left out. I was experimenting with handheld and lenses, and Rodrigo and I were on fire.”

The director found out that his 1 million feet of dailies were in storage in Mexico’s National Autonomous University archive. “I started exploring,” he said. “It was beautiful to see how, when I start seeing all [that] was left out, how many films were there within the film, and watching this material with a new gaze. When I was editing, I was watching with the function of finding the pieces of the puzzle to serve the narrative. But now I was seeing the flow and the beauty itself of the images, so without the dictatorship of the narrative, I start collecting. And that’s the beginning of this installation. It’s 35-millimeter projectors in a labyrinth of dark rooms, with these big guys projecting material like a magic lantern. It’s very dreamy. People are touched by it because it’s not an homage to the film. It’s a resurrection. It’s a reinvention itself, and it stays completely detached from the film.”

The essay reveals the context of the “Amores Perros” production, the director’s aesthetic and philosophy of filmmaking, and how he creates cards for each sequence in a movie. “My obsession is the grammatical film language,” he said. “Those cards integrate everything that I should know when whatever challenge of the film comes — in crisis, in production, in depression. Those are my bricks that sustain some clarity during [filming], and it helped me out. It’s an exercise that takes me days and months to get it all, but it’s homework that goes deep for me to understand what I’m dealing with. What is the purpose of the scene? What is the purpose of that character, what does the other guy want, and what will be the conflict?”

Mubi will re-release the film this month in theaters all over Latin America, and make it available globally on its streaming platform on October 24. While the filmmaker never made any money on the film, which he invested in, he now owns about 75 percent. “Mubi is buying the rights for the next 10 years,” he said. “They’re one of the few streamers that are supporting independent filmmakers. We are in the right hands.”

While the life of a filmmaker is peripatetic at best, Iñárritu and his wife, with their two children out of the nest, are trying to decide where to live. They’ve been residing in Los Angeles. “We are gypsies,” he said. “I did ‘Bardo’ in Mexico. So I lived in Mexico City for one year and a half. Then I finished shooting the last film at Warner Bros. It’s a difficult moment in the world, and that decision is important for us. Things have changed a lot, as you know.”