Incidentally, the other day I saw a guy in the subway train, who had his own bike in the train, but was also carrying a separate wheel in his hand. He didn't look very innocent to me...
Ha! That may have been me. I have been building my new bike at a co-op workshop, since I don't have all the tools/stand/space I need at home. I hardly bought any parts, as I've cannibalized my other stuff, a friend's old bike, etc, but that means at first I had to carry in not only my frame and fork, for example, but also the frameset from which I was removing the headset, etc. Carrying two frames over my shoulder, a wheel to true in one hand and a fork in another at rush hour, and having to switch trains at least once each way, I've gotten some funny looks (and other gestures.)