Now, I do know the New Haven had a yard in Springfield and did switch cars in Holyoke. And based on the map below they made it as far north as Williamsburg. My question is, did they use the River Line thru a trackage agreement with the B&M to interchange in Holyoke and to get to points north in Northampton and Williamsburg?
No, The New Haven had its own trackage, originally all the way up to Shelburne Falls. It was the former New Haven & Northampton Railroad and its connections, later known as the NH's Canal Line (so called because much of the line followed an old barge canal). Westfield-Holyoke is still active as the Pioneer Valley RR, which picked up the remaining track north of Westfield from Conrail. The "main" line to Northampton was also run by the PVRR as far as Easthampton into the 1980s. North of there to Northampton was abandoned in Penn Central days, although the NH right-of-way through Northampton is now a bike trail.
That NH map is circa early 1960s based on the line shown. If you find an older one, you'll see all the lines that once existed above Westfield.