Techniques for processing data include: receiving a hierarchical structure of metadata (MD) pages for a logical device; and performing processing to copy data of the logical device from a source system to a target system. The first processing includes: determining a sequence of the MD pages in accordance with a depth first traversal of the hierarchical structure; defining a cache management policy in accordance with the sequence that indicates when to load the MD pages into a cache and when to remove the MD pages from the cache; loading MD pages into, and removing MD pages from, the cache in accordance with the cache management policy; and copying data pages stored at logical addresses of the logical device in an order in which the logical addresses are accessed using MD pages stored in the cache at various points in time in accordance with the cache management policy.