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How would you go about proving the $(p, q, r)$ -pretzel knot is equivalent to the $(p, r, q)$ -pretzel knot?

By "equivalent" I mean you can change one knot into the other by elementary deformations.

I've found this question/example in several books and papers on knot theory where they state the proof as obvious.

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    Have you tried looking at a sequence of Reidemeister moves to get the $(p,r,q)$ pretzel knot from the $(p,q,r)$ pretzel knot? In particular you are trying to find an ambient isotopy. I think one can just use the definition of elementary deformation (e.g. look at the top of the second tangle and choose a point $P$ not collinear and try to deform it to the same section in the third tangle, etc...) So we keep moving down the second tangle.2011-02-17

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