There's not much analogy required, as he argued from "not a perfect copy", i.e., the existence of difference.
But are you saying you are being constantly destroyed and remade from one moment to the next?
No, but that intertemporal solidarity is my choice, just as someone's intertemporal solidarity with their teleported copy would be their choice.
You can choose to think whatever you like, but I don't think it changes the laws of the universe. You either have a continuous existence in time or you don't. You may decide that your Copy on Mars is you, but it is not. Your mind won't continue to operate on Mars if you shoot yourself on Earth.
Scott Aaronson has a new 85 page essay up, titled "The Ghost in the Quantum Turing Machine". (Abstract here.) In Section 2.11 (Singulatarianism) he explicitly mentions Eliezer as an influence. But that's just a starting point, and he then moves in a direction that's very far from any kind of LW consensus. Among other things, he suggests that a crucial qualitative difference between a person and a digital upload is that the laws of physics prohibit making perfect copies of a person. Personally, I find the arguments completely unconvincing, but Aaronson is always thought-provoking and fun to read, and this is a good excuse to read about things like (I quote the abstract) "the No-Cloning Theorem, the measurement problem, decoherence, chaos, the arrow of time, the holographic principle, Newcomb's paradox, Boltzmann brains, algorithmic information theory, and the Common Prior Assumption". This is not just a shopping list of buzzwords, these are all important components of the author's main argument. It unfortunately still seems weak to me, but the time spent reading it is not wasted at all.