Transporters work by de-assembling something (e.g. you) and re-assembling it somewhere else. What if, when you’re dis-assembled, you die, and the re-assembled version of you is essentially a copy? Then every time someone steps onto a transporter, their final thought before death is that they’ll end up beamed somewhere else. And the re-assembled version (copy) just thinks that everything went fine and continues on like nothing bad happened.
This was always my take on the matter, too.
I am my memories, my experiences, and the continuity of my consciousness, not the meat prison my mind is forced to reside in. If my consciousness continues, I am alive. Whether that’s this bag of meat, that bag of meat, or the Transmetropolitan-inspired nanite-cloud I wish I could live on as, I’m still me either way. There might be a difference, but from my perspective it doesn’t make a difference.