I assumed that the common mutations were the result of travel. Is that not the case? Is the belief that the virus is hitting the same mutations independently in multiple places?
While its possible some of it is due to travel, I've definitely read that there is plenty of reason to believe these mutations are arising independently in different nations. Basically the virus is mutating all the time, but the vast majority of mutations are meaningless or have negative impact on the fitness of the virus. However some mutations may be more commonly observed, either because certain mutations in particular regions are more common (due to the physics/chemistry of the proteins involved) or because the mutation changes the virus in a way that makes it more like to stick and ultimately spread among the population. Some of these mutations are basically like local minimums in a mathematical function, and its not uncommon to see random traversals of that function coalesce around these minimums, at least temporarily.