Opening in a Chain

With (parent) base disk B and children C0, C1, and C2, opening C2 gives you the contents of B + C0 + C1 + C2 (not really addition linked data sectors), while opening C1 gives you the contents of B + C0 + C1.

A better solution than recording base disks and which children are descended from which is changed block tracking, QueryChangedDiskAreas in the vSphere API. See Algorithm for vSphere Backup.