You have yourself quite the code. So many people have helped me along the way and like to make attempts to help others. However, I can only provide sources that will help you out.
A majority of the people here know what they are doing; considering no one has responded yet, let me point you to some ideas. From my research, many use plugins like turn.js or booklet.js
This site looks familiar to your code; however, it used transitions, but seems to be on the right path for your code;
You can check out this turn.js fiddle
You can download booklet
See if this one gives you an idea
I was going to have an animations page but with as many pages I had, it was easier just to allow my users to download to their computer, open in another page, and open in an iframe.
I’m sure a few of the others on here know how to perform what you’re asking. I am a great researcher, not so good programmer…yet. Sorry I couldn’t help more. I’m still learning myself and know what it’s like not getting help, any help is better than being criticized like other sites.