Changing class has no effect on selectors...

Changing class has no effect on selectors...

I want to change the behavior of a button by changing the class. 

On the first click, I see the alert" Step1: Class starts as Step1" as expected.
On the second click: "Step1: Class starts as Step2"

The class changes, but the selector seems stuck. What am I missing here?

Thank you!

$(document).ready(function () {

    $("#GoToNextStep").addClass('Step1');

    $(".Step1").click(function(e) {
        alert ('Step1: Class starts as ' + $(this).attr('class'));
        $(this).removeClass();
        $(this).addClass('Step2');
        alert ('Class set to ' + $(this).attr('class'));
    });
    
    $(".Step2").click(function(e) {
        alert ('Step2: Class starts as ' + $(this).attr('class'));
        $(this).removeClass();
        $(this).addClass('Step3');
        alert ('Class set to ' + $(this).attr('class'));
    });
    
});