From hyperbolic volume computation, I found that the following two 3-manifolds are (possibly orientation-reversal) homeomorphic:
- surgery on figure-eight knot $4_1$, with slope $-5$, and
- surgery on $5_2$ knot with slope $5$.
Is there simple way to show it using Kirby calculus? It must be easy but I am not that familiar with Kirby calculus.