1. A method, comprising: computing, in a local storage system having a local volume with a plurality of local regions, respective local signatures over the local regions; computing, in a remote storage system having a remote volume with remote regions in a one-to-one correspondence with the local regions, respective remote signatures over the remote regions; identifying for a given remote region having a given remote signature and a corresponding local region having a given local signature that the given remote signature does not match the given local signature; and replacing data in the given remote region with data from the corresponding local region.