rsync: is there an option to make rsync stop at first error so i can see what's happening?

ISSUE : I'm booted in a recovery mode and the recovery drive have no space left...

QUESTIONS : is there an option to make rsync stop at first error so I can see what's happening ?

Unfortunately, it seems rsync does not support this at the moment. There is an issue about this on GitHub: #71 rsync does not terminate when target disk is full. There, Wayne Davison (rsync's maintainer) writes:

Since this problem is inherent in the way rsync works and there is a work-around fix, I'm closing this bug. A future rsync 4.0 will hopefully not have this issue.

The issue also lists using --msgs2stderr as a workaround, you could try that, it should at least make rsync exit more quickly.