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I often have to edit the edges of polygons to match or be cut by the edges of other polygons with complex shapes. This sometimes leaves disconnected slivers.

Is there a simpler/faster way to remove these slivers (for example, like the "Eraser" tool in Paint)?

Currently, I make a graphic that contains the part I would like to erase, convert it to feature, and use "Clip" from the Edit menu to discard the area that intersects. Then I have to delete the feature layer that I just created for the sole purpose of erasing the sliver. This works, but is a lot of steps when you have to do it often.

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To remove gaps and overlaps you should use the Topology tool. The Topology tool helps validate your data based on different rules you choose appropriate. One of the many rules available in that tool is: (features) "Must not Overlap". The tool has an "Error Fix" button that let you zoom to the error (in your case, an overlap) and let you choose what to do - merge the overlap to polygon A or B? delete overlap? Ignore overlap (for false positives).

You should go to ESRI help: https://desktop.arcgis.com/en/arcmap/10.5/manage-data/topologies/an-overview-of-topology-in-arcgis.htm

Just FYI - your feature class/shapefile will need to be exported into a GDB and be contained inside a Feature Dataset to be able to run the topology analysis.

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If I understand correctly, you are trying to remove overlap between polygons. I would suggest looking at the ERASE and CLIP tools. If you are talking about slivers (gaps) between polygons, you can use the align to edge tool on the editor toolbar, as well as the snap tool. If you can provide screenshots of your workflow and examples of your issue I may be able to offer more in depth assistance!

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