I asked this question a long time ago. Since 2012, many applications have entered the market. I will list a few below and, as they are frequently updated, I deliberately avoid describing the pros and cons with the different ones. I have probably missed a few, please leave a comment with those who you think should be on this list.
Modern user interface design tools such as Sketch, Adobe XD and Figma have prototyping features that will allow you to create simple screen transitions.
Then there are tools like Adobe After Effects that will step up the level and make video effects as well as vector animations. But he will not make interactive prototypes.
For 3D interface animations, there is Blender, Cinema 4D, 3D Studio Max, and so on. But they are not usually focused on designing applications.