# Simple question on Kirby move

From hyperbolic volume computation, I found that the following two 3-manifolds are (possibly orientation-reversal) homeomorphic:

1. surgery on figure-eight knot $4_1$, with slope $-5$, and
2. 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.

$5_2$: Blowup at the clasp: Isotopy: Blowdown the purple unknot:
• I'm just claiming that the two links (above and below "Isotopy:") differ by a link isotopy in $S^3$. Just undo the kinks of the purple component (i.e. do Reidemeister 1 moves) dragging the golden component along. – Marco Golla Feb 1 at 23:55