Logo outline transparent for web

Question

I have created a logo. I did it with black fill and white lines. This works well for a white background, like in print; but for the web the white needs to be transparent so the background colors show through and where lines cross you can see the background.
I have tried using no-fill, but that makes the lines not delineated, rather than transparent. There are small bits with lines cross one another and to make their relationship clear I put in small white lines, which work well with a white background, but not for the web.
I'll attach a close up of the issue. I've offset the small line bits so you can see I'm trying to make one line cross another and where they cross have a clear line on either side of the crossing line.

Answer 1

KaCe,
As I (mis)understand it, you can:
1) Create both black paths with the Stroke Weight that gives the right widths, with the one that crosses over the other on top;
2) Select the top path and Object>Path>Offset Path by an amount equalling the visible gaps in the bottom path;
3) Select both the offset top path and the bottom path and in the Transparency palette flyout>Make Opacity Mask (Clip and Invert mask both unticked).
hat should give you a gap on either side of the top path.