The railroad name written on the side of the locomotive really has no bearing on where it can be assigned..
yes, they probably intend that a locomotive lettered Delaware Lackawanna will stay assigned to the DL, for the most part..
and a locomotive lettered DLWR will stay assigned to the DLWR, etc..but in reality, it often doesnt work out that way..
All the GVT lines swap power all the time, its very common..
They probably go back to Scranton if they need work in the shop that the local shops cant do..
then a DL locomotive might come up to western NY to take its place..and it might stick around for
awhile for any number of reasons..
the LAL lines also do this..
It just has to do with what power is needed where, and what power might need shop time.
The corporate parent company (GVT) doesnt really care what name is on the locomotive!
its more important that the trains keep moving..so they just swap locomotives around between the different railroads as necessary..
also, horsepower and size of a particular locomotive can be a factor on it being reassigned..
some locomotives are better suited to some railroads than others, depending on train lengths and etc..
so for efficiency, they might move a locomotive to another road, but not bother to re-letter it..
I think the current GVT NY state locomotive list is accurate here:
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someone please let me know if it isnt..