Anyone knows what kind of transition like this video?
What it is

There is no set name for this transition as it isn't a standard transition effect that you would expect to find as a preset in your editing software. It is probably a custom made transition sequence, however it's a rather simple one. It just takes the same image multiple time, applies different filters to them and uses a simple slide-in effect to iterate through them.

How to do it


Extract a frame of your video. 
You can either apply the different filters in an image editing program or in the animation software. I think the first method is easier. The filters used in the video you linked are pretty simple; for example, there's a black-and-white converted version of the frame in there, an inverted black-and-white version and one with crushed blacks, increased contrast and overall lowered brightness.
Import those versions of the still frame back into your project, put them in the timeline in quick succession (about 0.5 seconds per image) and apply the same slide-in effect to all of them (you can do this with keyframes, but you will probably also find it in the transition presets of your software).
(Optional) Note that the two instances of the transition you mentioned in your question are not exactly the same, they use different filters and effects interchangeably. For example, in the first occurance there's a grain effect applied to one of the still images and the whole transition sequence has a sepia coloration. The second instance uses a faded film look/effect for the last image in the transition. So you can customize this transition using different effects to have it look however you like. 


Why not to do it

Because it looks like crap. I have no idea what kind of video you are doing, but this transition will make you look like you just found out about Photoshop and decided to press all the buttons.
(cough Photoshop Philipp cough)

If you want your video to be taken seriously, use hard cuts or short, soft transitions only. In general, I wouldn't recommend trying to copy Hatsune Miku AMVs from YouTube, unless that is precisely the look and audience you want. Some more advice on transitions can be found in my answer here.