Unwanted Lines/Artifact appear when viewing a Fresco file on Illustrator

Hi!
When I send vector illustrations to Illustrator, I get a bunch of thin lines on my illustrations, like previous lines that were not erased accurately enough. 
They're invisible on Fresco, but very visible on Illustrator and take forever to clean up.
Is there an easy way to clean those lines or prevent them in the first place?

Thanks!!

Ayelet.

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