To get rid of the ones you have already received :
Use your web browser to log on to your account
There should be a search box on the web page (on mine it is above my list of most frequent/recent contacts). Click on that box and you should then get a drop down menu which includes an option for Advanced Search. Click on that option.
In the From box, type Amazon Local
Down at the bottom there is an option to enter how far back in time the search is to be done, with the default being 3 days if memory serves. Click on that box and select the 1+ year option.
Click on the OK or Search button.
You will then get a list which only contains the emails from Amazon Local. There are about 35 to a page, with a little box beside each entry. Above the list there is another tick box which will select all the entries on the page. Click on that, then select Delete.
Repeat the select all+delete process until you have deleted all of them, or until you get fed up with it, whichever comes sooner.
If you find that you cannot unsubscribe from those emails, flag the next ones which arrive as Junk and they will be put into your junk folder automatically, and you can then empty that folder every now and then, or wait until they are deleted by Live Mail, which I think happens after 30 days.