Topological quantum physics - spin statistics

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Replusz
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TL;DR Summary
"In the left picture with the loop, we have two identical particles that change places. "
I don't understand why this is true. If I understood correctly, those pictures show a (one!) thick piece of string forming a loop and then pulled. How come particles are exchanged?
From: (page 13)
http://www-thphys.physics.ox.ac.uk/people/SteveSimon/topological2016/TopoBook.pdf

Any help is greatly appreciated! Thank you! :)
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