Thanks for the reply

It's geodesics that are the problem.

Take a simple example.

A survey sets up a theodolite at point A on the earth's surface and sight point B.

He then sets out a line of pegs leading to B

Another surveyor sets up at B and does the same thing.

This produces two rows of pegs leading from A to B and B to A.

This is well known and derives from the fact that gravity at A and B point to slight different centres since the Earth is not a true sphere.

I am trying to get my head around the more difficult question of the universal spacetime manifold, which does the same thing on a much grander scale than the 2D manifold of the Earth's surface.