Where does equality and communism apply in Animal Farm?

The irony of this question is that there isn't communism or equality in Animal Farm. 

At the beginning of the book, Old Major, spoke of Animalism.  In the way he expounded it, there was equality or something akin to communism. For example, there was no class distinctions among the animals. Pigs were not better than horses, and horses were not better than dogs. This corresponds in some ways to Marx’s vision of communism where the proletariat are equal with everyone else (bourgeoisie).

In addition, within Animalism, the animals no longer work for capitalistic humans, like Mr. Jones.  To be more technical the animals own the means of production and the outcome of it. And the land belongs to the all the animals. 

The ideas of Animalism are great, but as the story progresses, the lust for power makes it unable to work.  Napoleon becomes a tyrant.