Do the thread contributors think there should be as many direct rail links between Liverpool and Manchester as can be between Glasgow and Edinburgh?
At least one route needs to be four track. It's not the number of two-track railways that matters, it's the ability to mix meaningful frequencies of fast and slow trains, and that means a four track railway. Or a dedicated non-stop line.
Given the size and proximity of the metropolitan areas along the Liverpool - Manchester - Leeds axis, I'd say it needs around 8tph fast trains (not TGV speed - 110 or 140mph EMUs would be fine), plus a metro-style stopping service along each pair of slows.
The service aspiration should be to enable half of all households in Liverpool to reach Central Manchester within 60 minutes, and vice versa. That's the best way to achieve the agglomeration benefits which deliver economic growth.
From Liverpool to Manchester, the fast lines could go via Warrington Low Level, which could provide a regular 8tph fast service calling at Liverpool, Warrington BQ, Airport HS, Piccadilly, then on to Huddersfield, Dewsbury, Leeds.
But I think it would be better to provide the fast service by quadding the Chat Moss route. A twin-track tunnel from the M60 to Salford/Victoria would be aound 5 miles, around half the length of the HS2 tunnel from Davenport Green to Piccadilly. Would also need tunnels from Wavertree Technology Park to junction 5 of the M62, around 3 miles. And shorter tunnels going East to Standedge
It would make more sense for HS2 to approach Manchester from the West too, but that is a separate discussion.