Canyon formation animation // help

I have a canyon made with a heightmap.
I want to make an animation where a smaller canyon transforms into the canyon formed with the heightmap.

Is this possible ?

Sounds like a job for an animated height map!

Create a series of images that morph from one canyon to the next. Then drive a displace modifier using that image sequence.

That’s a good idea, but, the landscape would morph into the each other or simply change ?

It would morph in proportion to the number of frames you created. If you only have the start and ending states it would simply change. So pull out your after effects and make a few in betweens. There are other morph programs as well, including Blender itself.