Topological relativity?

Relativity says that 2 observers can each see relative length contraction when observing the other.

In other words, I could see that I could fit your house inside my house, and you could see that you could fit my house inside yours. Practically it would be hard to do... with special relativity, it would require the houses to be moving very fast relative to each other. Parking houses is a difficult manoever at near-c speeds. With general relativity it might be possible with some weird gravity thing that I don't understand. Maybe it involves being on opposite sides of an event horizon. However, is it even possible? Or does topology give a reason why it isn't?

Seems to me, if you have one thing topologically "inside" another thing, but you have control over space so that you can compress one part of space to an infinitesimal length, and inflate another to infinite length, you should be able to turn the whole thing inside out (and even treat it as simply a change in point of view, if you had that power), without changing the topology of the set of 2 things.

So could we not then have universes inside our universe? Possibly black holes are entire universes that we see only as something infinitesimal. Perhaps even, just like 2 houses each inside the other, perhaps we are topologically inside these black hole universes. Could we be inside each of the black hole universes that are each inside of us? It's not that we're some tiny dot within the tiny speck that is a black hole singularity, each recursively within a larger version of the other, but rather we're both inside and outside of each black hole depending on which side you turn out... like a reversible jacket with billions of insides and maybe just one "outside" that one can see at a time. Your universe, whichever it may be, is always seen as the outside in the normal perspective of life.

Perhaps falling through an event horizon feels like that, like a reversibile universe turning itself inside out, so you fall into the "outside" of a different universe, and the universe from whence you came turns into an "inside", and becomes a black hole that resides within your new universe. Of course, you'd probably feel a lot like Hawking radiation, and uh... be it... which would probably put a damper on your ability to look around and contemplate how much like a jacket the multiverse seems.

They should teach topology in grade school. Then by first year of university, kids would probably know the answers to these questions.