Concur with all the advice given above - attempting to transit the Canadian border with any firearm can be costly and is definitely ill-advised. There are a lot of other things to consider as well, so you should thoroughly research entry requirements early in your trip planning in regards to what is or is not allowed; requirements on pets, what you've stocked in the fridge/pantry, etc.
Also be aware that any sort of criminal record beyond a speeding ticket can prevent your entry (all members of your party are subject to background check at the border). For instance, a DUI is considered a felony in Canada.
It would really suck to drive all the way to the border only to be turned away - especially if you shipped your piece to Anchorage. There are ways to document your "rehabilitation" for your particular crime (why do I feel like I'm quoting Arlo Guthrie?) if any, but that could be costly and time-consuming as well.
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