Here's the gist of my hunch: Biosphere is all that is physical, ideosphere is all that is mental, and the animosphere is all that is spiritual (term I made since it has a sphere and animo=spirit since I felt spirit realm wasn't scholarly).
Biosphere would involve all the instincts, chemistry, physics, biology and so-on.
Ideosphere would involve all thoughts, beliefs, feelings, memes and possibly code and so-on.
Animosphere… just speculating since I have no magical experience but I would guess it is the source of true free will, souls, God or THE ALL though THE ALL might be all three realms embodying one single being, genuine magic, thalmaturgy/miracles, illumination and maybe enlightenment though enlightenment might be obtainable in the ideosphere.
I'm aware of the 7 spiritual realms mentioned in esoteric communities and the odd varieties of realms from Buddhism. I simply am venturing to guess, they don't exist and were purely created with creative intentions rather than out of self-experience.
I don't know magic, but if it's real it comes from the animosphere. The ideosphere would be where all the technological and symbolic progress we've experienced comes from. The biosphere would be where all the evolutionary physical progress we've experienced comes from. Enlightenment and illumination appear to be two different things and though illumination would definitely exist in the animosphere if it exists while I would guess enlightenment is potentially reachable in the ideosphere though it could also be exclusive to the animosphere just as illumination would be.
Bottom line is all this magic stuff on Fringe, if any of it even is real, is probably exclusively accessible to people who can break into the animosphere and I have no idea how to access any of that and thus am forced to simply entertain it as a fun thought rather than promote it as a personal experience.