A Skirmish between Magpies and Carrion Crows

On Monday I travelled to work via Ascot rather than via Farnborough North.  While waiting for the train to leave Ascot, I watched the following  little skirmish between a pair of magpies and a pair of carrion crows. 

One of the crows was perched near the top of a conifer tree and one of the magpies, I'll assume it was the female, was rather agitated and repeatedly flying up to the crow, obviously trying to drive it away from the tree.  The other crow was in the lower branches of the conifer and the other magpie was in a nearby silver birch.  The second crow repeatedly flapped up to the second magpie, presumably the male, apparently also trying to drive it off.  After a minute of two of this, the two crows flew off.  The female magpie immediately flew to the top of the conifer and went into it.  After a few seconds more the male also flew upto join her, with a twig in his mouth.

What were they fighting over?  I suspect that it was a nest that the magpies were building.  Maybe the first crow was inspecting it with a view to taking it over.  I don't think that the crow was raiding eggs, firstly the crow was not deep enough into the tree to be eating eggs, and secondly there was no sign of egg on its beak.  The fact that the second magpie carried up a twig does suggest that they were still  building the nest.