How to control podman's images with git?

We are using podman's containers for the project. The issue, we have is what while working on different branches of the project we need slightly different containers. So each git branch has its own container building script. But the images for these containers are not under git's control. So after each git switch we need to rebuild containers, which can take a few minutes each time. Is there a way to *conveniently* put podman's images under git's control? Is there a how-to for this somewhere in podman's documentation? How is it solved (if it is solved) in other container systems?