Which airlines need to hold interline agreements with each other in order for an itinerary to be bookable?

I was poking at ITA Matrix out of curiosity, and tried to find flights from Shungnak, AK to Hyannis, MA. Theoretically, this would be a 6-stop flight (there are other possible itineraries as well, but assume the seasonal JFK-HYA service on jetBlue isn't a thing for this):
- Shungnak to Kobuk on Ravn Connect (operated by Hagelund Aviation)
- Kobuk to Kotzebue on Ravn Connect (operated by Hagelund Aviation)
- Kotzebue to Anchorage on Ravn Alaska
- Anchorage to Seattle on Alaska Airlines
- Seattle to Boston on jetBlue
- Boston to Hyannis on Cape Air
However, ITA Matrix cannot find an itinerary for this, and I suspect it's because of interline agreement issues. This brings us to the larger question, though: which airlines in an itinerary need to have interline agreements with each other to make an itinerary bookable?
Is it the case that the marketing carrier needs to have interline agreements with all the operating carriers? Or can you book a flight in a case where all the carriers have an interline agreement with at least one other carrier, but there is no carrier that has interline agreements with all other carriers in the route? How does this work, for a US flight?
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