The story is pretty good if you can follow whats happening however, to the normal viewer its hard to keep with the twists and turns. One minute you think you have it all worked out than suddenly, something else is revealed that makes you rethink the entire thing. At least it ended pretty good compared to other anime.
The animation is some of the best I have seen (To be fair though, I haven't watched many anime renowned for having great Animation). It looks great throughout and shines during the fight scenes. From the epic op to the final fight the animation is superb.
The op "Serendipity" is amazing, with the stunning visuals and the beautiful track. This is one of the few animes I watched the op everytime. The ed is ok at best though. It has some nice little clips but I found myself skipping it often due to wanting to move onto the next episode.
To sum up Flip Flappers, it is an anime with a confusing but intresting story, stunning visuals and a relatively good soundtrack.
