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This set of features are owned lands that have been individually added as features, naturally they aren't perfectly placed

I have fixed every big overlap and now only small lines overlaps are left, but 4074 of them! Here's an example :

enter image description here

I know there are similar questions here, I don't know if I did them wrong but they didn't work, I need the polygons to remain closed, individuals and the number of features can't change and changing the cluster tolerance affects everything else.

I want to merge for all topology errors, choosing either to receive the merged area, maybe a python code to iterate the topology errors?

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    Did you try Integrate? you can specify the tolerance. – klewis Jul 12 '16 at 18:13
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Yes, use the integrate tool but make a backup copy of your data since this tool will alter the geometry. For example, if you have a polygon smaller than the tolerance the polygon will collapse.

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