MySQL MERGE Implementation

Question

There are two tables in my MySQL database which have a many-to-many relationship. There is a third table which handles it, with the foreign keys of the first two.

I need to update the relationship. I may have to add a row with a new relation and delete a row that represents a relation that does not exist any more. To take track of the changes, I created a new table that contains all the relations that are valid, and does not contain the old ones that are meant to be deleted.

There is a lot of content on this MERGE statement for SQL, which would solve my problem:

https://www.sqlshack.com/sql-server-merge-statement-overview-and-examples/
https://codingsight.com/merge-updating-source-and-target-tables-located-on-separate-servers/
https://www.sqlservertutorial.net/sql-server-basics/sql-server-merge/
https://www.educba.com/mysql-merge/

The problem is that for some unclear reason MERGE does not exist in MySQL. It kinda has an alternative, called INSERT ... ON DUPLICATE KEY UPDATE, but it is not the same and does not cover what I am aiming here. I don't want to delete all the relations on the table and re-insert the new ones.

I would like to know if there is any other alternative to MERGEin MySQL, or any way to "add" it to my database.