TITLE: Simple question on Kirby move
QUESTION [7 upvotes]: 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.

REPLY [16 votes]: Yes, there is a simple way. Below is a sequence of pictures illustrating the procedure (created using Kirby calculator).
$5_2$: 
Blowup at the clasp: 
Isotopy: 
Blowdown the purple unknot: