Unwanted white lines around all overlapping shapes

I made a hand written logo in illustrator and I am animating it in after effects to look like it is being written, revealing the logo. I am using the stroke effect with reveal original image selected. Because the handwriting has thick and thin parts of the same letter, I had to split the letters into multiple layers. However, now when I animate them, there is a faint white line wherever the layers overlap. This shows in the preview and after rendering. They do not show up in the original file in Illustrator. How do I get rid of these?