What's the Name of That Book??? discussion

I know that the main character was a teenage boy and that he often thought about his little sister, who had some kind of cutesy name that ended in an “-ey”, and how much he missed her while time traveling. I think he jumped to try and save someone who fell onto the tracks?

In one time travel incident he gets arrested and then bailed out by either the Irish or Italian mob because of his last name, and he then works as an indenturer. I think it was an Irish last name the more I think about it?

In another incident he time travels to the Great Depression. He talks about the homeless people all over Central Park. He goes to buy a burger and the guy at the counter says “please, it’s been 2 days,” and they split the burger. Later when the protagonist is starving and crying on the street corner, his friends are trying to comfort him and a wealthy woman discretely hands them an apple to give to him once he’s collected himself.

The last time travel era is during WWII. He runs into his friend he shared the burger with while on a bus or train or something, and the man is now in uniform and missing an arm.

In the end he travels back to the present the same way he came, by falling into the subway tracks. He’d saved the persons life and is reunited with his little sister in the end.

I would’ve read this sometime around 2010? Give or take a few years.

Backtracked

I turned to face him. A lone tear traveled down his cheek. "It's been three days," he whispered.

I had never seen anyone cry of hunger, much less a guy who could be my brother or my cousin. I felt sorry for him and worried for myself. "Would you like some of my burger?" I broke off a chunk and handed it to Mick. "You can finish the fries. I'm not hungry anymore." It wasn't true, but I knew a guy more desperate than me when I saw one.

Wow! How did you find that so fast, I’ve searched for so long!!! Thank you! 😍

No problemo! I actually found it by searching Worldcat, keywords "subway," "juvenile," and "time travel."