One 4-car set runs from Liverpool to New St. Another runs from Crewe to New St via Stoke. They meet at New St and join to form an 8-car train to Euston via Northampton.
This is an utter inter-related mess and it is all going to end in tears just like Northern. Having seen just how complex it is, I now strongly oppose it. It shouldn't have been done until enough units and crews existed to keep the diagrams separated and simple.
As an example of how it should be diagrammed to be reliable and have adequate capacity for the extra demand the through working will bring, there should be a self-contained set of 8-car trains and crews (with an extra 4 to bring to 12 south of Northampton at peak times) operating nothing but Euston-Brum-Liverpool and vice versa, with the same calling pattern both ways.
If that wasn't possible (as I suspect it wasn't), the service should not be operated.
So for the sake of simplicity, the service from Crewe joins the service from Liverpool to form a Euston?
Is it the same northbound? The Crewe via Stoke splits from the Liverpool?
Is there a split involving the Rugeley too?
Also which set will arrive at New St first? The one from Liverpool or Crewe? Likewise northbound which heads north first?