That being said, it depends on what you want to do. If you are looking for a central backup of multiple MySQL servers, you can run a single machine with multiple instances, each acting as a slave to an individual remote server.
If you want a central analysis machine without two-way replication (data just comes from the remote servers), you could script a process where each remote server ships data to the central machine, or makes it available for pulling. Then the data can be loaded into a central MySQL instance which is used for analysis.
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