This one is going to be more tricky.
Imagine a sphere with two linked handles. Is it homeomorphic to a sphere with two unlinked handles? Well, you know the classification theorem, so you know that the answer is “yes”. But can you actually imagine a gradual, continuous deformation that unlinks two handles? (If you do, you must have an extraordinarily good spatial imagination.)
Solution (it involves creepy, googly-eyed men with no legs):