When compressed into a single word, 'anytime' is usually an adverb. Like: "He's about to arrive anytime."
In the sense of "You're welcome!" I would use "any time":
"Hey, thanks mate!"
"Sure, any time!"
There aren't very strict rules for it, to be honest. Except when you say: "I won't have any time until Friday." Then it definitely needs to be two separate words!