How to merge common parts of qemu qcow2 disks

I have a qemu image B.qcow2 that is a snapshot of A.qcow2. I created a copy of B.qcow2 by using cp B.qcow2 C.qcow2 and then worked on both B.qcow2 and C.qcow2 independently. Thus, B.qcow2 and C.qcow2 are eventually different but they have a common part (since C.qcow2 was copied from B.qcow2). In order to save disk place, I wanted to know if it is possible (by using qemu-img or programmatically) to create another image common.qcow2 that will contain all common parts of B.qcow2 and C.qcow2, then remove this common part from B.qcow2 and C.qcow2 and rebase the images in such a way that B.qcow2 and C.qcow2 are based on common.qcow2 and common.qcow2 are based on A.qcow2?