I have designed a logo in InDesign and exported as PDF to open up in Illustrator to be saved as AI and EPS file, as well as PNG and JPG. There are white layers (from original "effects" applied to the design in InDesign) showing up when I import the EPS file into another InDesign file and place on a color background. I have tried ensuring my colors are all process but that didn't do it. Obviously, I don't know enough about what I'm doing to troubleshoot myself ... help!
EPS doesn't support live transparency—transparency gets flattened when you save. You could try flattening on the PDF export (PDF/X-1a) rather than on the save, or better yet give up using EPS.
EPS doesn't support transparency.