In pulling back the curtains, Amazon, one of the most private public companies in the world, revealed how it is racing to piece together an immensely complex puzzle—much of which it is having to build from scratch, at giant expense and with painstaking attention to the minutiae, as it tosses out assumptions that American customers have taken for granted for decades. In doing so, the company, an upstart here, has thrown itself into a knife fight with two privately owned and much more established Indian competitors [...] as well as a clutch of smaller Indian startups that are nipping at all of their heels.