Anytime Vs Any time

Anytime (one word) means whenever or at any point in time
Any time (two words) usually mean any amount of time

Example: if you say "I can go for a swim anytime tomorrow," you are saying that you can swim at any point in time within the day tomorrow. If you say "I do not have any time to swim tomorrow," it means that you do not have any amount of time tomorrow to swim as you are busy with other work. 

One point to note is that if you use 'anytime' with 'at,' you should always use the two-word form. So, both these sentences are interchangeable:
"I will go for a swim anytime tomorrow" or "I will go for a swim at any time tomorrow." 

More examples:

1. The sick man will pass away anytime.
2. You can ask me questions anytime and I will answer them when I have any time.
3. The rain might fall at any time.
4. I can visit my mother anytime.
5. Did you call me at any time yesterday? No, but I will call you anytime today.