Thank you for this post because it was useful.
What I did in the end is to handle the swipeleft / right events at the level of the document, not in my pageDiv.
Nevertheless, binding to the swipeleft event I do it at the level of the pageDiv using the pageshow event. This is because I want to handle the swipe differently only for this page, not for any other. I think doing so is just playing safe...
I paste some code for anyone interested:
$("#pageID").on('pageshow',function(evt){
$("#bodyContent").css("-webkit-transform", "translateX(0px)");
$("#bodyContent").css("-moz-transform", "translateX(0px)");
$("#bodyContent").css("-o-transform", "translateX(0px)");
$("#bodyContent").css("-ms-transform", "translateX(0px)");
$("#bodyContent").css("transform", "translateX(0px)");
$(document).on('swipeleft',function(event, data){
event.preventDefault();
// more code here
});
});