I've seen in the text the construction of a 'flask' 4-manifold described by adding a punctured 4-sphere to a tubular end $S^3\times \mathbb{R}^+$. Also it is said in the context that this manifold itself admits an orientation reversing isometry and gluing two copies of it together along the tubular ends should give a diffeomorphic copy of $S^4$.
How do I see this? I can't even imagine how do we attached the punctured 4-sphere to the tubular ends.