Three baby mice took up residence in a small aquarium after the tragic Victor-ization of their mother. The plan was to keep them until they could be released into the wild, but their cuteness got the better of the plan.
The cage soon needed changing, but catching mice to transfer them is as hard as picking up drops of mercury with your fingers.
Habitrail (TM) would do the trick but it's pretty dear for temporary pets.

Soda bottles make a cheap and robust set of skyways and nesting chambers.

Step 1: Cut a Hole in the Mesh Top.

A square hole, with diagonal cutters.
Smaller than the bottle top.
I cut at the corner to make butting two cages together, but the bottles can go anywhere.

Step 2: Screw in the Bottle

I left the bottle cap ring on this bottle, because I wanted the threads to still be engaged in the wire mesh when the bottle was screwed all the way in.

Step 3: Cut a Hole in the Side of That Bottle

Take out the bottle from the mesh top.
Cut a round hole about the size of the inside diameter of the bottle top.
Then cut a series of radial slits to about the outside diameter of the bottle top.

Step 4: Screw Bottle Into Bottle Side

I removed the ring from the horizontal bottle, so the flange would sit flush.
I was going to glue this, but it didn't need it.

Step 5: Assemble Transfer Link.

By following steps 1 through 4 for both aquarium/cages,
and cutting the bottoms off of the horizontal bottles, a link is made between the cages.
Put the food and toys in the clean cage, and overnight, the mice explore and make their move.

Step 6: Mouse Nest in the Sky

Once the necessity of changing the litter is relieved, only one aquarium/cage need be on the table.
Replace the open-ended bottle with a whole bottle. Melt about a hundred holes in the bottle with a skewer heated in a candle flame or alcohol burner flame. Add a couple of sheets of tissue paper, and the pent-mouse apartment in the sky is ready for occupancy.
Replace the bedding as necessary.