What does Hempel mean by "homotopy 3-cell"?

Question

I am reading John Hempel: 3-Manifolds (specifically Lemma 6.5 on incompressible surfaces) and struggle to find a definition of what a homotopy 3-cell is.

Does it mean "an open 3-manifold that is homotopy-equivalent to the interior of a 3-ball"? Does it include simple connectedness at infinity? Is there today an easier definition / characterization (e. g. in the presence of the Poincaré conjecture)?

(For instance, Hempel also uses the term homotopy 3-sphere for what we can now simply call a 3-sphere.)

Answer 1

As Moishe Kohan stated in his comment it means a contractible compact 3-manifold with $S^2$-boundary, a reference being

C. H. Edwards Jr.: Products of pseudo cells. Bull. Amer. Math. Soc. 68(6): 583-584 (November 1962).