New York Jets center Connor McGovern (60) during second half...

New York Jets center Connor McGovern (60) during second half of the Philadelphia Eagles at the New York Jets on October 15, 2023. Credit: Lee S. Weissman/Lee S. Weissman

FLORHAM PARK, N.J. — The Jets don’t consider the Giants their bitter rivals the way they do the teams in their division. It’s more of a sibling rivalry and the Jets want to play the role of big brother.

The Jets will be the visiting team when they play the Giants at MetLife Stadium. The game definitely has extra meaning for the Jets. They will go for their third straight win — and some bragging rights — when they face the Giants on Sunday.

“You have to be a rivalry in the same city,” defensive end John Franklin-Myers said after practice Wednesday. “You got to be the big brother, little brother, whatever that is. But at the end of the day, shoot, I want to be the winner. I don’t give a [expletive] about no big brother, little brother, small, medium or large. I don’t care about none of that. I want to win.”

Which one is the big brother and which is the little one?

“We’ll see Sunday,” Franklin-Myers said.

It is a big game for both teams.

The Giants (2-5) are coming off a home win against the Commanders.

The Jets (3-3) are coming off their bye and want to continue the good feelings they had before going into it.

The Jets came back from 11 points down to beat the Eagles. The Jets’ defense held Philadelphia scoreless in the second half and sent the reigning NFC champs to their only loss this season.

This game on Sunday could have similar passion and intensity because these two teams share a building and play each other every preseason.

The events of their last game could lead to some additional juice.

When they met in August, Aaron Rodgers and Giants defensive end Jihad Ward exchanged shoves and some words. Ward later said he believed the Jets were laughing in the huddle after a Randall Cobb block gave Giants safety Bobby McCain a concussion. Rodgers disputed that and said Ward is “making up.”

It’s doubtful either team forgot what happened, but this game probably would be spicier if Rodgers were healthy. He tore his left Achilles tendon in Week 1. Rodgers will be in the building and probably on the sideline for the 15th regular-season Jets-Giants game.

“You’re kind of claiming for the city,” Jets center Connor McGovern said. “It’s a fun crosstown rival, same stadium. It’ll be a little weird being on the opposite sideline for a game. Every game’s important. Maybe this one carries a little bit more bragging rights. It’s a big game.”

For the Jets, it’s important to get off to a good start coming out of the bye. The last two years, they lost their first game after their break.

The Jets were 6-3 at their bye last season and ended up 7-10. That collapse led Robert Saleh to change up the practice and meeting schedules this week with a focus on keeping the players fresh for the stretch run, hoping it will lead to different results.

The Giants have had their own struggles, but they have played better the last two weeks. They nearly beat the Bills in Buffalo before their win over Washington. Their defense is definitely playing better. The Giants have allowed a combined 21 points the last two weeks. They didn’t hold a team under 24 points in their first five games.

“They’re playing a lot better,” Saleh said. “Defensively, you guys know how much respect I have for Wink [Martindale] and what they do. They’ve been making it very hard . . . They’re getting better every day. They’re starting to look a lot like that team that made the playoffs a year ago.”

The Jets’ goal is to not look like the team they were after the bye last year. They shouldn’t have a difficult time getting up for this game.

“When it comes to rivalries, it doesn’t quite hold the same weight like the AFC East rivalries do,” McGovern said. “You always want to win and be the better team. If you need a little extra motivation, you can find it.”

The Jets don’t want to be the little brother on Sunday.

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