You can't really have "independent operations" on a bank account.
If node A sees deposit,withdraw and node B sees withdraw,deposit one of those is business-as-usual, the other is overdraft. You can't have a "high availability" system where some parts of the system are acting like it's okay, and other parts aren't.
Not everything is a bank, but a lot of things are often more-like-a-bank than they first appear...