Another thing to suggest to your doctor is that s/he look in any standard medical reference guide (the doctor should have some online one), where oxygen is the #1 recommended abortive.
This is all oh so true. In my opinion, O2 is not prescribed for reasons that have nothing to do with its efficacy (which is unquestionable), or even the insurance issues (though they definitely state this as a reason, as CHChris says). It's because most docs have no experience with patients using high-flow oxygen, and there are unsure about how to prescribe it and what to do with a patient who is using it. So you have to persist. Even that is not always sufficient. Government insurance programs (Medicare, Medicaid, VA) are not allowed to prescribe O2 for CH. This is an irresponsible abomination. I think any private insurance has to cover it (could be wrong!) but it can take a lot of work to get them to do so. Maybe you want to call your insurance co in advance to get an idea. If your doc gives you the insurance "excuse," you might say you want to get the prescription anyway and you'll pay out of pocket if you have to.
Regarding suppliers -- as CHC' suggests, you should call them after you get your prescription and make it clear what CHC' says: a large tank and a small one, with regulators for each (they use different regulators) that go up to at least 15 lpm, and non-rebreather mask. You do not want a "concentrator," which makes O2 out of room air. I haven't heard of docs prescribing tank sizes, but maybe it happens, and that would be good. The supplier is going to make a lot of runs to your dwelling to replace tanks if they give you only a small one or a couple of small ones. There is also a ,mask very strongly recommended for people with CH, which you will have to buy yourself: http://www.clusterheadaches.com/ccp8/index.php?app=ecom&ns=prodshow&ref=clustero2kit And you might want to get higher-flow regulators. We can discuss that when the time comes.
Fingers crossed that it will be as easy as it should be, and not as hard as we have come to expect it to be.