The AGPL requires that you publish a
notice that the source is available
on demand to the people who use your software over the network. The easiest way to do this is usually to just publish your changes so you can link everyone to it, but that is not a requirement of the license.
You can run derivative AGPLv3 software to service the public without distributing your changes to the source code without violating the license as long as nobody asks for the code.
