Is it possible to do something like this:
with two video sequences in the video editor or elsewhere in Blender?
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In short: you could do it manually by morphing tesselated plane with video in texture from one shape key to another. If sequences have no highly significant difference then it would look more or less acceptable.
This tutorial will help you: http://www.blendernation.com/2014/01/06/morphing-photographs-with-blender/
Yes, you can but it's awkward if you want a high-quality morph. For each frame, you need to create a plane with a material that blends from one frame image to the other. Mark distinguishing features with vertices for the first image, then save as shape key. Move vertices to mark same features in second image, save as second shape key. UV unwrap each shape key and map to each image in the material. Blend equally between shape keys and textures progressively through the videos.
When you use the word "morph" it implies some processing that is not a feature of blender.
The closest thing blender can do is that you can animate the transparency of one video strip so that the video strips beneath it are revealed. This is done with title cards pretty often (although title cards are usually static, they are still strips in the VSE).