The Azure search api offers a fuzzy paramter for suggestions. like this:
https://blssuggestions.search.windows.net/indexes/cities/docs/suggest?api-version=2015-02-28&suggesterName=default&fuzzy=true&search=berlen
Would return "Berlin" as a result of berlen.
I can't find a documentation about this how to activate it in a normal search setting there fuzzy = true seems to not change anything
https://blssuggestions.search.windows.net/indexes/cities/docs?api-version=2015-02-28&search=berlen&fuzzy=true
[Update]: Please see the other responsed about using querytype=full as this response is no longer correct.
This is correct. Fuzzy search is only available currently in the suggestions api.