No, not if their content is identical (or very nearly so), and they all have a canonical link element referencing www.mysite.net
.
However, that sort of issue happening site wide can be considered a crawl efficiency issue and the canonical link element doesn't really solve that. In your example, a search bot would crawl three pages when it really only needed to crawl one. Scale that up, and add other duplication issues, and it gets to be a problem.
So for that sort of issue (we can include things like with/without the www subdomain, with/without HTTPS, etc.), it's usually better to use URL rewrites to 301 redirect back to the canonical form.
The canonical link element is the weapon of choice when there's a lot of variation in the duplications you're managing, or you don't know in advance what they will be. Think of a shopping site where tens of product category refinement parameters can be added to a base URL in any order, for example. That doesn't mean don't add it unless you have that sort of problem, just don't rely on it to solve problems there are better solutions for.
mysite.net
as referenced in the first answer. Subsequent edits toexample.com
would break that reference, howeverexample.com
can be considered the same.