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In case of Peer to peer replication, if Master goes down, will the other two nodes continue synchronizing or not?
In a Peer-To-Peer replication topology all the nodes are master. So, there is no concept of just ONE master.
The image in your question seems to be made up and wrong. See original doc.
Read up more on - Peer-to-Peer - Transactional Replication
Required, but never shown