Applying to jobs in other provinces, being in Toronto

Hi, I've been applying to jobs all over Canada (Tech/IT), as I'm open to relocate. But employers seem to prefer someone already living there. On my resume I've been mentioning my location in Toronto, and Willing to relocate, but I'm not getting any interviews. My LinkedIn also mentions Toronto. I can change that, but I've been applying in different cities (Montreal, Ottawa, Vancouver, Calgary etc).

How should I go about it? Should I update my resume accordingly to the job location, though I'm not living there? And what about the location on LinkedIn? Thank you!