How do i retain a transparent background when i apply a filter to image in Photoshop?

[otori_katsumoto]

I erased a bunch of stuff on an image and it was fine and kept the transparent bg when i saved it as a jpg, but when i applied a filter to it, it had a white bg when i saved it and there was nothing i could do about it. What can i do to prevent this (it shows a transparent background but when i save it it has a white background)?