Tracking clicks on each link separately I have create a website that, on the same page, will offer several links to the exact same section (node).
For example the link to the "Contact us" node appears 3 different times (in 3 different places) on the home page.

Is there any way to track each click separately and to know which links were clicked to reach the contact us page?

I am already using the "Google Analytics" Drupal module, but the same link is tracked as a single unit, regardless of the number of times it appears on a page.
You can append a different query string to each link, which will allow you to track each one individually. Lets say your contact page is at mysite.com/contact. You can create several url's with a query string that lead to the same page. Ex:

mysite.com/contact?link=1

mysite.com/contact?link=2

mysite.com/contact?link=3

etc.

You can always append a query to a URL without creating any aliases or anything. Simply add ?key=value (obviously you can change 'key' and 'value' to anything you'd like). Google Analytics will track all of these separately.

The only downside is that Google Analytics won't batch all your contact page visits under 1 url anymore, but instead each different query will be listed separately.