Merge multiple backups of the same database schema

I have about 200 copies of a SQLite database. All taken at different times with different data in them. Some rows are deleted and some are added. They are all in a single directory.

I want to merge all the rows in the table my_table, using all the .db files in the directory. I want duplicate rows to be deleted, showing all entires from all the databases, just once.

I'd like to do this in pure SQL, but I don't think it's possible, so we can use Python too.