Animus is the manifestation of the fifth element, Spirit. Mana is some sort of cosmic glue that both binds elements together, and keeps them separate, like an invisible film to keep them from completely mixing if my understanding is correct. How much is present varies from reality as they each have their own rules. The link will in some instances occur naturally as Animus will often draw mana towards it, wizards however often do the reverse in using mana to draw animus towards them. They use mana to attract any desired element which they desire to use for their spells and then manifest.
I am not an expert and am basing this on my knowledge of astlanian magic.