I have a basic question which I am not able to figure out. If we do a Gluck twist on a nullhomologous 2-sphere in a 4-manifold, it is said that it does not change its intersection form. But as far as I understand the Gluck twist changes the framings and knotting of the link components which represent the second homology. So why doesn't the intersection form change?
Basically this is Lefschetz duality. Chopping out the neighbourhood of the 2-sphere gives a 4-manifold $X$ with boundary $Y = S^2 \times S^1$. You can think about the intersection form here and how this will change after the surgery.
The point of $S^2$ being null-homologous is that if you look at the long exact sequence on homology (say) of the pair $(X,Y)$ you will see that every element of $H_2(X,Y)$ is represented by a unique element of $H_2(X)$.
I think it's necessary that the $S^2$ be null-homologous, I would imagine that otherwise, a priori, the intersection form may change.