The kinetics of water filling and emptying the interior channel of carbon nanotubes is studied by molecular dynamics simulations. Filling and emptying occur predominantly by sequential addition of water to or removal from a single-file chain inside the nanotube. Advancing and receding water chains are orientationally ordered. This precludes simultaneous filling from both tube ends, and forces chain rupturing to occur at the tube end where a water molecule donates a hydrogen bond to the bulk fluid. We use transition path concepts and a Bayesian approach to identify a transition state ensemble that we characterize by its commitment probability distribution. At the transition state, the tube is filled with all but one water molecule. Filling thermodynamics and kinetics depend sensitively on the strength of the attractive nanotube-water interactions. This sensitivity increases with the length of the tubes.