References needed for Dehn surgery and Kirby calculus

Question

I learned from Colin Adams's book, $\textit{the knot book}$, that every compact connected three manifold comes from Dehn surgery on a link in $S^3$, and if two different Dehn surgery yield the same manifold, they must be related through some operations called Kirby calculus. The book give no proof or references for that. Would someone give some references ? I want to know every detail of it. Thank you.

Answer 1

If you are asking for the original references:

• Wallace'60, Lickorish'62: every 3-mfd is obtained by surgery along a framed link in $\mathbb{S}^3$
• Kirby'78: two manifolds $M_L$ and $M_{L'}$ (obtained by surgery along $L$ resp. $L'$) are diffeo iff $L'$ can be obtained from $L$ by Kirby moves.

Of course, proofs can be found in many books, lectures which are more recent. (e.g. Saveliev'98 or Prasolov, Sossinsky '97).