I don't know of any modules that build this functionality inside Drupal itself. However, there are several tools out there, for which there are Drupal modules, that allow you to visualize the *arc* that you speak of. Two of my favorites are:

**MixPanel:** [Mixpanel][1] can allow you to create funnels that will help you see how the user is progressing through your website. For example, how many logged in users clicked on a product, how many of those went on to the payment page, and how many of those actually ending up paying. Mixpanel also has a Drupal module for easy integration. Or you could easily integrate this using a custom Mixpanel module with minimal effort. This is how a funnel in MixPanel would look like:

![mpflow](http://tctechcrunch2011.files.wordpress.com/2011/09/funnel.png?w=640)

**Google Analytics:** It has a fantastic Visitors flow functionality that will allow you set flows, goals, and track against those too. Again, Google Analytics has a readymade Drupal module. Here's what a flow in GA would look like:

![gaflow](https://4.bp.blogspot.com/-tqf1dlIuUNk/Tp75LWwogqI/AAAAAAAAABc/Q8tf9sHLqrk/s1600/VisitFlowpart1.png)

  [1]: https://www.drupal.org/project/mixpanel/