Any closed 3-manifold is a boundary of some compact 4-manifold.

Question

I knew this is true:

Any closed, oriented $3$-manifold $M$ is the boundary of some oriented $4$-manifold $B$. See this post: https://mathoverflow.net/q/63373/27004/

I heard this statement is true:

• Any closed 3-manifold is a boundary of some compact 4-manifold.

Can one show this and explain it intuitively?