Your second animation looks fine to me. The first however...
It looks like an existing "
transparency optimised" animation was incorrectly processed causing the optimization to become white!
OR the transparency index information was lost!
If the pure white is a unique color you could map that color to transparency,
Try this...
convert bad.gif -transparent white fixed.gif
Or use a lowlevel program like giftrans
http://www.ict.griffith.edu.au/~anthony ... /#giftrans
to find the white index and specify it as being transparent.
the latter will make the least impact on the animation but is harder to do
Hmmm that did not work right! the color is not always pure white, and the timings in the animation is horrible, relying on the web browser's minimal time sequence (bad idea). Display this in IM "animate" or some other GIF animator and you get the animation zipping through so fast it is all a blur!
The best idea is probably to unpack the animation into individual frames and animation meta-data using say "gif2anim"
http://www.imagemagick.org/Usage/scripts/gif2anim
fix each frame so the 'white' parts become transparent, the repack using the reverse "anim2gif"
http://www.imagemagick.org/Usage/scripts/anim2gif
examples of using this script is in IM examples, Animation Basics
http://www.imagemagick.org/Usage/anim_basics/#sequence
But is also used in Animation Modifications.