White lines appear on PDF after saving from Illustrator file

I am working on a series of illustrations for a book. The graphics are complex, containing several clipping masks, transforming effects (mirorring, rotating, copying etc.) and different kind of objects such as shapes, lines with stroke, brush tool etc...

In the illustrator file it looks exactly how it supposed to be, no white lines, no other strange things. But after i saved it to a PDF file, white lines appear. It seems like in the shape of the clipping masks, but not all of them. I tested it on a simple home printer, and the white lines were visible on the paper also, probably they would be there after the final printing process...which i would like to avoid. I saw that a lot of people had similar problems, and i already tried a bunch of suggested solutions. None of them was useful unfortunatelly. Any suggestions? Thank You!