I assume you're asking because you're performing actions before the compose that automatically rasterize the graphics without transparency so you can't just do ImageCompose[gaxes, gbig].
Try this:
blck = ImageCompose[ColorNegate[Rasterize[gaxes, Background -> None]],
ColorNegate[ImageCrop[Rasterize[gbig, Background -> None]]]]
Also, you don't need to specify the GIF file format when exporting, since it's already in the file name.
Apologies if I'm not interpreting your question correctly.
