Do supply lines work together?
Solution 1:
Yes, supply lines are commutative and transitive. Reflexive too, I suppose. This makes it an equivalence relation, meaning that you can see the same supplies at all connected settlements.
In other words, if you set up a supply line from Sanctuary to the Red Rocket Station, and one from the Red Rocket Station to the Starlight Drive-In, you can access the supplies from all three locations at all three locations.