Spectators inside North Greenwich Arena gasped at the height when he peeled off the bar toward another orbit and when he caught the bar by his fingertips on the way down.

Alvarez put on his own show, performing the routine earthbound from his vantage point on the floor. He swayed, he straightened, he stuck out a foot, windmilled an arm.

When Leyva landed, he and Alvarez knew it was brilliant. Alvarez ran around like he was being chased by a bee.

“Yesso!” he yelled, his term for yes and eso.

All the toil had been worth it for this moment. Alvarez and Leyva’s mother, Maria Gonzalez, were members of Cuba’s gymnastics team who defected to Miami in 1992 and 1993. Alvarez worked odd jobs, saved money and sought donations to open his gym, which has grown to 150 pupils.

Even as an asthmatic toddler, Leyva wanted to do gymnastics. He won his first meet when he was five years old. He fell off the high bar, but convinced judges – behind Alvarez’s back – to let him get back on.

“Everything I owned when I crossed the river is better than anything I have now,” Alvarez said, referring to when he swam naked across the Rio Grande with only a plastic bag that contained his clothes. “I can be the poorest person in the world, but I can say I don’t like the president if I want to say it. It’s about freedom. This medal is a bonus.”

Alvarez said he didn’t doubt Leyva’s ability to get onto the podium, even after the lousy 13.5 on horse.

“It’s like my team is in the ninth inning, the other team has 11 runs and we have zero, two outs and everyone is leaving the stadium,” Alvarez said. “But I know we going to win. That’s how me and Dani think.”

Leyva uses his lucky towel, which now has its own Twitter account, to block out scores.

“I lie to him and say the horse score was great, the judges were nice to you,” Alvarez said.

Said Leyva: “That’s my dad. What else would he say? He knows how to motivate me. But I saw the score and I knew it was bad. So I put the towel over my head and went, ‘Grrrrrr!’ ”

His mother, watching from the stands, kept willing Leyva to be patient. She’s the calm counterbalance to the exuberant Alvarez.

“Dani gets so mad – I saw his face, like a baby, after horse,” she said. “But his P bars was amazing. Dani is like that – when he makes a mistake, he turns the page.”

His medal helped make up for a disappointing fifth place finish in the team competition Monday.

“This was redemption for the whole team,” Leyva said. “I’d like to dedicate my medal to my coach, my mom, my grandparents, my teammates and everyone back in Miami. But I’m not satisfied with bronze. I’ll come back in 2016 looking for gold.”

Leyva was asked what it was like trying to beat Uchimura, the so-called Michael Jordan of gymnastics.

“Yeah, but I’m Danell Leyva,” he said with a smile. “I’m not trying to copy him. I’m trying to perfect me.”

As Leyva stood on the medal podium, he took deep breaths and beamed as the theme from “Chariots of Fire” played. Alvarez wasn’t allowed on the floor, but if he had been, he would have been doing cartwheels.