Animate multiple Body parts without Seams Acting Weird

When you have multiple gameobjects/body parts attached to the same rig and try to animate that rig, it often has distortions at the seams, i.e. the bottom edge of the torso freely detaches from the top edge of the trousers, and there's a big hole in the overall mesh.
How do you get around this, does anybody know of a way which doesn't include using a single game object and mesh?

Look at the neck area of this mesh for an example of what I mean, there's a hole there due to the animation.

uploaded file correctly apologies
look at the neck area for an example of the problem