Yankees GM Brian Cashman good-naturedly pranks Red Sox manager Alex Cora

NEW YORK – “The Rivalry’’ got pretty intense last month in Boston, but it produced a lighter moment before Tuesday’s Red Sox-Yankees game.

During Yankees batting practice, Red Sox manager Alex Cora, Yankees manager Aaron Boone and Yanks general manager Brian Cashman were chatting idly behind the cage. The trio suddenly burst out laughing, punctuated by Cora bear-hugging Cashman, lifting him off the ground.

A witness said it was a reaction to Cashman placing an “I Heart Phil Nevin’’ sticker with a Yankees logo on Cora’s back.

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After the Yankees and Red Sox brawled on April 11 at Fenway Park, Yankees third base coach Nevin made some pointed remarks to the Sox’s coaching staff and later shouted in the direction of Boston’s dugout.

Cora responded by gesturing to Nevin that he go back to his coaches box.

“To tell somebody to go back and get in their little box, everybody saw that,’’ Nevin said at the time. “That’s pretty unprofessional.’’

Cora felt Nevin had crossed a line by screaming toward his dugout, citing a “chain of command’’ breach.

“I don’t know if he was screaming specifically at me,’’ Cora said at the time. “And I took exception.’’

Greg Bird update

At Tampa, Fla., Yankees first baseman Greg Bird (right ankle surgery) batted in a second straight extended spring training game on Tuesday. “(He) felt really strong,’’ Boone said, adding that “probably any day now’’ Bird will begin a minor-league rehab assignment, either at Class A Tampa or Class AAA Scranton/Wilkes-Barre.

“He’s moving in the right direction,’’ Boone said of Bird’s mid-to-late May ETA in the Bronx. “Now it’s about how his rehab goes, how he’s bouncing back every day, building up to nine innings, playing back-to-back days, finding his stroke. Hopefully, it’s not too long before he’s back with us.’’

David Price-less

Boston lefty David Price was scratched from Wednesday’s start and sent back to Boston due to numbness in his pitching hand. Seton Hall Prep grad Rick Porcello moves up to take Wednesday’s start, with lefty Eduardo Rodriguez now starting Thursday’s series finale. Price had exited his April 11 start against the Yankees after one inning (four earned runs) due to the same issue.

Jacoby Ellsbury delayed

Boone said that outfielder Jacoby Ellsbury was sent home Monday due to illness at Tampa, Fla., where he’s been rehabbing. Ellsbury is still “a little ways off’’ from getting into extended spring training games, according to Boone, but “hopefully he’s on his way’’ soon. Since spring training, Ellsbury has dealt with a strained oblique, a sore hip and plantar fasciitis.