Question:

Is there an event for Amazing Slider when slide changes?

Answer:

Yes.

$(document).ready(function(){
   $("#amazingslider-1").bind("amazingslider.switch", function(event, previous, next){ 
     console.log("previous:" + previous);
     console.log("next:" + next);
   });
});

In the above codes, the amazingslider-1 is the div ID of the slider. If you have specified a different ID in the publish dialog, you need to change the number accordingly.