In my experience, there's no need for glue of rivets when making a 'trangia-style', or 'pepsi-can' burner.
If you make the lower, outer can come up the full height of the burner (at least to the 'shoulder' of the upper, inner can), then it will act as a full-height fuel cup.
Also, when the shoulder of the inner can meets the rim of the outer can, it forms a pretty robust interference fit that is adequately gas tight, provided there are no dents in the shoulder.
Having a joint in the middle of the sidewall of the burner is the weakest place to put it; the flexible sidewalls bend easily at this point. Putting the joint at the shoulder of the inner can is the strongest place, since the shoulder is the strongest part of the can (take an empty can, and see how much force it takes to press the sidewalls in in the middle of the wall, then try the same at the shoulder...).
Here's my set of instructions for making a 'classic' burner using this sort of joint.