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I am trying to understand the following inequality, $$0 \leq \tau (K_{+}) - \tau(K_{-}) \leq 1$$ from the following paper by Livingston. \ https://arxiv.org/pdf/math/0311036.pdf . At page 737 , he argues, a negative crossing change converts $-T_{2,3}$ into the unknot.So $(K_{+} \# -T_{2,3} \#-K_{-})$ bounds a disks with 2 double point. Resolving the double point we get a genus 1 surface. I am trying to construct an explicit movie from $K_{+}$ to $T_{2,3} \# K_{-}$ with a genus one cobordism between them. I end up having a genus 2 cobordism instead of 1. Please help me with the movie move.

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See Livingston's "Computations of the Ozsvath-Szabo knot concordance invariant" (https://arxiv.org/abs/math/0311036), Corollary 3.

Or see my thesis for a picture of Livingston's cobordism (p. 19, http://lewark.de/lukas/PhDthesis-Lukas-Lewark.pdf).

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