Snapshots may be remotely replicated asynchronously from a first LSU (R1) on a first storage system (A) to a second replica LSU (R2) on a second storage system (A2). The storage system A1 may open a consistency window to suspend initiating processing of new write operations received on A1. While the consistency window is open, A1 may: take a first snapshot, SS11, of R1; record, in association with the first replication cycle, an indication to replicate SS11 on A2; and initiate a next replication cycle to record write operations of the next new write requests to be received from hosts. After initiating a next replication cycle, A1 may close the consistency and transmit the first replication cycle to A2. A2 may apply the write operations of the first replication cycle to R2, and then take a second snapshot SS12 of R2, which should be a replica of SS11.