For the reference:
In order to move between two different the battle grounds (or the "network"), here is what to do...
1. Visit the correspond "access point". (*I didn't check to see if you have to go in the access point, or just unlock the map section that contains it will do.*)
2. In case the initial battle ground is "Cancer" and you wish to move to "Gemini". In the battle ground, move your Shinki to the blue vortex first. (Your Shinki has to stand on it to make the jump.)
3. As your Shinki stands on the vortex, click to select the point - the first option on left menu should now become "Move to other Network".
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So far so good, haven't met anything crazy in the Cancer or Gemini. (The AGs in both are easily beaten, no sweat.)
One thing that catches my attention is the item parts called "Otome circuits"... (It's the same name from an old old anime

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