How to strip special characters out of string?

I have a set with the characters I allow in my string:

var characterSet:NSCharacterSet = NSCharacterSet(charactersInString: "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLKMNOPQRSTUVWXYZ")

I want to strip any other characters from a string so two unformatted data can be considered equal, like this:

"American Samoa".lowercaseString == "american_samoa1".lowercaseString

the lowercase version of these transformed strings would be "americansamoa"