Note: technically none of these reactions is "correct", or, in a way all are "correct", depending on what you mean by "correct". Technically, as Hunter pointed out, this is sum of several processes, this always means more than way of balancing the reaction equation in terms of having the same number of atoms on both sides of the equation. That doesn't mean reaction proceeds following the equation, paper will accept anything you write, reality will do its own thing
The book solution is more or less equation that describes the whole process as performed in the industrial synthesis of the acid. It lets you estimate the process stoichiometry with a reasonable accuracy, but in practice process will never exactly follow the reaction equation, it will be always off.