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I've seen a merge animation in a mobile game which you can check here;

https://youtu.be/G7l24Wtdcxw

You can observe the animation when the tiles combine.

Can it be done in Unity3d, may be using shaders? Or, do I need to use a 3d app like Blender?

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This is done by covering/swapping the tiles with another set of tiles that will be animated, replacing them on screen, then playing animated tiles in sequence.

You will need to prepare animated tiles.

They can be animated in many ways: Scaling the GameObject with a script, shaders modifying the pixels opacity and/or model scaling, pre-animated meshes (e.g.: In Blender), procedurally animated meshes, animated texture sequences, animated vector graphics (e.g.: SVG)...

Which way to use to animate depends on your preference, available tools, skill set, artistic direction, and which is "best" is entirely a matter of opinion (Questions that demand opinion-based answers get closed).

However, no matter which animation technique you use this is the sequence of events to achieve a similar result to the video linked:

enter image description here

The red overlay tiles are transparent for demonstration purpose. In reality you'd want them opaque to cover the original tiles.

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