New York Mets pitcher Anthony Kay during a spring training...

New York Mets pitcher Anthony Kay during a spring training game against the Atlanta Braves at First Data Field, Saturday Feb. 23, 2019 in Port St. Lucie, Florida. Credit: Newsday/Alejandra Villa Loarca

PHILADELPHIA — Ten years after he was first drafted by them, Stony Brook native Anthony Kay reached the majors with the Mets on Sunday, the latest twist in an on-again, off-again engagement between player and team and a particularly eventful several years for his career.

The Mets first selected the lefthander in the 29th round in 2013 out of Ward Melville High School, the same school that produced Steven Matz, then a mere pitching prospect for the club.

After Kay attended UConn instead of going pro, the Mets selected him in the first round in 2016. He spent time in their minor-league system before they dealt him to Toronto as part of the Marcus Stroman deal in 2019.

Now the player and team are together again for a late-season look, with Kay serving as a fresh arm in a Mets bullpen that needs it.

“This is our third try now,” Kay, 28, said with a laugh before the Mets lost to the Phillies, 5-2. “I feel like we’re in a bad relationship. So hopefully this one lasts, and ends a little bit better than the first two tries.

“It’s crazy. I got [designated for assignment] two Mondays ago and then got a call on Wednesday saying that I got claimed by the Mets. That was probably the last team that I was expecting that to happen, especially so late in the season. I thought I would’ve just gone unclaimed or something like that and I was going to go home. But here we are. I’m just enjoying every second of it.”

Kay entered with one out in the sixth on Sunday and retired four of the five batters he faced, striking out two in 1 2⁄3 innings. He hit Kyle Schwarber, who was erased on a double play.

Kay bounced between the majors and minors with the Blue Jays and Cubs for parts of five seasons. For part of this year, he was teammates with Stroman, a fellow Long Islander. The pitchers talked about their transactional connection “all the time,” Kay said.

The Mets claimed Kay off waivers from Chicago on Sept. 14. He owns a 5.49 ERA and 1.61 WHIP in 42 major-league appearances.

Since he last was a member of the organization, Kay has become a “completely different” pitcher, he said. He dumped his curveball in favor of a cutter and sweeping slider. And — new this year — he swapped out his signature glasses for contact lenses.

“Everything is so different now,” he said.

Kay had a 3.76 ERA in Triple-A this season. In two appearances with Syracuse, he tossed 3 1⁄3 scoreless innings and struck out eight of 11 batters.

He characterized this cameo as “hopefully kind of a tryout for next year.”

“He’s pitched well down there,” Buck Showalter said. “I’m anxious to see him. I’ve heard some good stuff about him. So we’ll see. There’s a need there.”

A veteran of the Mets’ farm system at a time when they were well behind industry norms on technology and other resources, Kay returned with interesting perspective.

“I can already see the insane improvements that they’ve made over the last four years, and I’ve only been here for a week,” he said. “Very excited to see what they have up here [in the majors] and see what they can do for me.

“It’s just, like, little things. The food, the nutrition side, the strength coaches and everything like that. You can tell they’ve made so many steps forward toward trying to make everything better here.”

Notes & quotes: Brandon Nimmo was absent from the lineup Sunday because of a right hip/leg bruise suffered Saturday on a slide into the plate. Showalter said Nimmo said he should be able to play Tuesday . . . The Mets assigned righthander Peyton Battenfield to Syracuse to make room for Kay, but because Syracuse’s season is over, Battenfield will just go home . . . Starling Marte (right groin strain) wound up not going on a rehab assignment with Syracuse over the weekend because of the bad weather. He still might return to the active roster this week.

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