I've never made, or even seen, one of those animations   

But my guess is that you want them side by side in a double wide video?

That, then, would depend on what video editing software you use.

It would be easy in adobe after effects and possibly premiere or sony vegas.

What software do you use for video editing?

OK, since you said "sequences" and not "compositions" I assume you're using premiere.

I rarely use that since I am so much more comfortable in After Effects, so I'll tell you how I'd do it in AE and hopefully the technique will carry over.

You didn't correct my guess that you need both image sequences playing side by side, so I'll assume that is how this is supposed to work  (remember - I have Zero experience with 3D Video, but I can guess!).

I would import both image sequences to AE.  Then make a composition from one of them by dragging it to the main window.

The go to Composition > Composition Settings and change the width to 2 times whatever it currently is.  If I started with the left half, I'd drag it all the way to the left.  Then just drag the right half to the timeline and position it all the way to the right.

Add to render que and done!

OK, what am I missing?

It can't be that simple, can it?

Maybe you need some space between the two videos?  Just add some pixels to the width in your comp settings and reposition the sequences.

Maybe there is something I am totally unaware of and am thus unable to give a good answer.

If there is more to it than that, just direct me to an example and I'll see if I can figure out what they did.

I did warn you that I never even saw such a video  (probably because my dyslexia keeps me from seeing 3D like you normal people!).

I have made a quite complete stereo video tutorial here:
http://www.fractalforums.com/tutorials/stereo-animations-with-mandelbulb-3d-stereophoto-maker-virtual-dub-and-youtube/

Here a playlist with my stereo videos:
https://www.youtube.com/playlist?list=PLA52c3hK9X7Gtqtqc2_NQK2v1OYUgb9fR

They are all uploaded right-left format, but YouTube now only supports left-right format  So maybe you have to flip your glasses to see them correct. Another way is to install a YouTube Flash-HTML5 switch add-on. The old YouTube flash-based-player had much more stereo options (also flipping sides) than the newer HTML5 player.