Excellent question. Airlines have been all over the map on this question for a number of years. Some forbade all stoves, some allowed clean stoves and of course no fuel, some varied their policy on a day to day basis.
But in the wake of the Sept. 11 attacks, indications are that all airlines have clamped down on packing stoves with luggage. Frankly, I think this is borderline ridiculous. The fuel limitations were of course always understandable; I could even see the rationale behind barring fuel bottles that were empty but that smelled of fuel. After all, gasoline vapors are highly volatile. But a clean stove? I don’t get it.
Anyway, you probably can assume that if you try to pack your Superfly, it will be plucked from your baggage, thrown against a wall, frisked, and questioned by hard-eyed men wearing dark suits (“Admit it, you boiled water on the Appalachian Trail, right?”). Of course, you always can call your airline ahead of time and see if you can receive dispensation. Otherwise, you’d better count on purchasing a stove in Belize. And you’ll likely be better off with a liquid-fuel model there, anyway - something like a Whisperlite International ($75) that can burn white gas, standard auto fuel, and kerosene. You might also be able to get away with packing a brand-new, never-used stove.