The two verbs
are near-identical synonyms. They are, in fact, identical as to their denotations. People may disagree, however, as to the equivalence of their connotations. For example, when we hear or read anschauen we simultaneously hear or read a faint echo of the noun Anschauung in the back of our mind. There is Weltanschauung but not Weltansehen. Similarly, there is Ansehen (reputation) but not Anschauen (reputation).
Discussion of the question whether there can ever be wholly-equivalent synonyms can get very heated, so I'll end by saying that in my opinion, people sometimes do choose one of the verbs over the other, but based on a very subtle gut feeling and one that they usually would not be able to explicate if asked.
The "too long, didn't read":
Yes they are interchangeable and especially for you as a language learner this is something you need not worry about.