All three are moth larvae, however butterworms will never transform into moths. All butterworms leaving Chile, the place where they grow in the wild by eating the tebo plant, are irradiated to prevent them from turning into moths. This helps prevent them ever becoming an agriculture problem in the country they are exported to, but also prevents raising your own.
Silkworms and waxworms can both be raised fairly easily. Both require fairly expensive food, with the silkworms requiring either fresh mulberry leaves or the powdered chow, and waxworms requiring a mix that has honey/bee pollen in it, and so most people avoid raising them. Once you have the colonies going, and a constant supply of food, it's quite easy to keep them going. Most people run into a bump when they run short on food, or try to change the colony to a new kind of food after it's established, both of which can crash the entire thing.
Basically, you want to keep them warm, with plenty of food available constantly, and with the silkworms you're going to want to clean them regularly, maybe every week or so, so that mould and bacteria do not build up in the colony, as this could crash them. Most people remove the cocoons into a separate bin for them to lay their eggs, and start new eggs in a new clean bin for silkworms. Most people let waxworms become a self-sustaining colony with all ages and sizes in one bin.
That's the basic just of it, but there are tons of sites out there that get more in depth about different methods you can use.
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Rob St. John
Canadian Feeders
http://www.canadianfeeders.com/