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I looked at that Uuni last time you posted it, and it looks interesting. As I looked at it further and read a bit about it however, you will notice that it burns some kind of proprietary wood pellets, and my guess it goes through a tonne of them to stay at high temperature. The one layer of steel isn't going to hold much heat. So while the oven would be easy to carry, the fuel and pizza ingredients would likely be prohibitive for moving by bike. I would think anyway.
http://uk.uuni.net/collections/frontpage/products/uuni-2
would defo fit on a rack on a bike...