Footnote: A Mama Dog always knows her babies. If the people say they don't have the mother dog.... ask them where they got the babies and from who.
Maybe it could be verified that way. But again (as several people have stated) who would leave them in the first place. It is very suspicious that 4 people say that they belong to them.
Maybe these babies would have a better chance in life if good homes can be found for them by people like you,,, rather than by people who would lose or leave them. I just know that if I had ONE baby puppy, let alone THREE, it would never leave my sight, I would know where it was. And it wouldn't be in some shopping cart. Sounds like maybe they were trying to give them away (with no luck) and didn't want to take them back home so they left them. Please keep us posted. Thanks.
Good luck to you.