# Obtain 4-manifolds by repeating surgeries of submanifolds in $S^4$

In his paper QFT and Jones Polynomials, Witten states: "It is a not too deep result that every 3-manifold can be obtained from or reduced to $S^3$ (or any other desired 3-manifold) by repeated surgeries on knots." (page 383).

Is there an analogous statement/theorem for 4-manifolds? Such as obtaining other 4-manifolds by repeating surgeries of submanifolds in $S^4$? What new 4-manifolds can be obtained in such constructions?

What are the obstruction to obtain any 4-manifolds from repeated surgeries of submanifolds in $S^4$?

References are very welcome.

If an $n$-dimensional smooth manifold $X'$ is obtained from $X$ by doing some surgeries, then there is an $(n+1)$-dimensional smooth cobordism $W$ from $X$ to $X'$; vice-versa, any handle decomposition of such a cobordism induces a sequence of surgeries.
In dimension 4, the oriented cobordism group is isomorphic to $\mathbb{Z}$, the isomorphism being given by the signature. For example, $\mathbb{CP}^2$ is not obtained from $S^4$, since their signature are different (1 and 0 respectively).
It is a theorem of Iwase that every 4-manifold can be obtained from a connected sum of a number of $\pm CP^2$ and $S^1\times B^3$ by surgery along tori: