You need to get some carpenters wood glue in the crack from the top.
After it settles in a little, then push, if you can, the steps back up tight.
Wipe the glue that squishes out with a damp, not wet rag.
Let them set before you use them if you can.
or stay out of the middle of the treads.
If the tread will not push up tight, you may have to tap it in with a hammer.
Don't pound it too hard, just snug it together.
You could also glue permanent blocks on the bottom of the treads and use a clamp to draw them together. This of course takes more time.
If you notice squeaking from the sides,
you can stuff thin flat shims in the sides where the steps attach.
Try to resist using nails if you can.
You risk splitting the treads and having to replace them.
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