I want to fully understand the process used to create antiX Linux from MEPIS Linux. I have pieces of the puzzle, but I don't have it all put together.

I understand that the scripts for creating antiX Linux are at
========= SCRAPER REMOVED AN EMBEDDED LINK HERE ===========
url was:"http://www.mepisimo.com/antix/Tarballs/"
linktext was:"http://www.mepisimo.com/antix/Tarballs/"
====================================
. I can see the source code for the installer, the extra IceWM scripts, etc.

I'm still not clear on how you start with a MEPIS Linux ISO and end up with an antiX Linux ISO. Since Swift Linux is based on antiX Linux, I think there is a lot I need to learn about the process of creating antiX. Can someone shed some light for me?

anticapitalista is the guy for that.
What I can say is that antiX shares with MEPIS the kernel, but maybe not much more than that (even the repositories don't work as the MEPIS ones are made for Debian stable).
I know that antiX has a live system (way of booting live and installing to HD). I think that BitJam is the one that designed it. Maybe it was once based on the MEPIS one, maybe it's still a similar system, I don't know. The antiX installer was at first the MEPIS one and now I know it's a modified version but I don't know how much and I think I read talks about antiX having its own installer.