Pairwise Choice Markov Chains (PCMC) have been recently introduced to overcome limitations of choice models based on traditional axioms unable to express empirical observations from modern behavior economics like context effects occurring when a choice between two options is altered by adding a third alternative. The inference approach that estimates the transition rates between each possible pair of alternatives via maximum likelihood suffers when the examples of each alternative are scarce and is inappropriate when new alternatives can be observed at test time. In this work, we propose an amortized inference approach for PCMC by embedding its definition into a neural network that represents transition rates as a function of the alternatives' and individual's features. We apply our construction to the complex case of airline itinerary booking where singletons are common (due to varying prices and individual-specific itineraries), and context effects and behaviors strongly dependent on market segments are observed. Experiments show our network significantly outperforming, in terms of prediction accuracy and logarithmic loss, feature engineered standard and latent class Multinomial Logit models as well as recent machine learning approaches.