DOES MANA REGEN WORK WITH BLOOD MAGIC?

I'm new to POE and I'm wondering if I have a decent amount of mana regen and choose the Blood Magic passive, does that mana regen work towards regenerating my life? I would think it doesn't, but it would be pretty cool and surprising if it did!

Also, the same goes for Eldrichs battery... Does that mana regen work towards my energy shield?

If you have Eldrich battery you don't have any energy sheild to regen.
But mana regen does help regenerate your mana that you have instead energy sheild. Mana regen works great with Eldrich Battery.

If you have blood magic, you don't have any mana to regenerate. So mana regen is useless.