In the first case, the first part of the saga would be the order processing service sending an event to the supply service. This one would do its part and send another event to the payment service. The payment service would then send yet another event back to the order service. This would complete the transaction (the saga), and the order could now be happily shipped.
If the order service would want to track the state of the transaction, it would simply need to listen to all those events as well.
Of course, sometimes the order would be impossible to complete, and a rollback would need to happen. In this case, each step of the saga would need to be rolled back separately and carefully, as other transactions could run in parallel, for example, modifying the supply state. Such rollbacks are called compensating transactions.
This way of implementing the saga pattern is pretty straightforward, but if there any many dependencies between the involved services it might...
