Answer: Probably not, but ask your DM.
3.5e is notorious for not defining things regarding spellcasting. Nowhere is it defined exactly what a spellcasting class is. PHB 1 p. 174 mentions the following:
Names of spellcasting classes are abbreviated as follows: bard Brd; cleric Clr; druid Drd; paladin Pal; ranger Rgr; sorcerer Sor; wizard Wiz.
These are all the spellcasting classes in the book, making "being able to cast spells" a possible definition of a spellcasting class.
But are Theurge classes spellcasting classes?
There is no definition regarding what an arcane spellcasting class is. Some will tell you that you have to cast arcane spells to be one, others say that it is bound to the classes themselves (bard, sorcerer, wizard). Looking at the mentioned spellcasting classes you have to be able to cast spells to be a spellcasting class. Theurges do not get spells on their own: instead they grant spellcasting levels in other classes rather than getting their own. This would mean that Theurges are not spellcasting classes because they don't have their own spells, and thus do not qualify as arcane spellcasting classes.
But because of the incredible vagueness of the wording involved it could be possible that you can use one Theurge class to serve as the basis for another. Given the large number of classes involved, however, your caster levels will not be on the same level as a solo-class character of that same level, making your magic less potent. Entering a Theurge class the hard way (Wizard 3/Cleric 3) is seen as undesirable given how far your levels will fall behind. A Wizard 3/Cleric 3/Mystic Theurge 10 will give your 16th level character casting like a 13th level Wizard/Cleric, giving you access to your 7th level spell as opposed to a Wizard 16 or Cleric 16 who is about to hit 9th level casting. As such, while you can cast quite a diverse scala of lower level spells your firepower will be limited.
If you present this to your DM and ask for permission to use Mystic Theurge as levels for Anima mage, and point out that it would not result in a game breaker, there is a fair chance your DM will let you play this character.