Vespucci provides basic facility to resolve version conflicts on upload. In general is it best to avoid them happening, particularly in areas with lots of editing activity by downloading only small areas, refreshing them often and saving changes frequently.
The OSM API reports conflicts one by one. The upload will abort at the first error and you will need to resolve that and then re-upload, fix the next issue and so on, exceptions noted below. If you suspect that your edits have caused more than a handful of conflicts you can save the edits either by saving to a JOSM compatible OSM file or by exporting the changes to a OSC file and then try to resolve the conflicts in JOSM, if you prefer using a desktop computer.
The most common conflict is when an object has been modified or deleted while you were editing and the version number of the object that you modified is lower than the current one on the OpenStreetMap servers. In such a case you will be presented with the options to cancel, or resolve the issue by
While Vespucci attempts to avoid this happening, a referential conflict can occur when you delete an object locally, and the server still has objects that refer to the deleted one, which haven't been modified accordingly or you have local elements that refer to elements that have been deleted on the server.
In the first scenario you can resolve the issue by (for each element)
In the second scenario, you can, again per element
This is the easiest to handle conflict and Vespucci will automatically retry the upload after removing the deleted element from the to be uploaded data.