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The polygon coverage is built and cleaned, but shared edges still draw twice.
Even though polygon coverages have topology, the ArcGIS drawing framework does not leverage this. Each polygon is drawn separately, so any shared edges are drawn twice.
The problem appears when using cased or patterned lines.
There are two possible workarounds depending on the type of symbols used.
In ArcGIS 8.3 you can use topology to create non-overlapping line features based on polygon outlines. For details, follow the link under Related Information.