In the case of Montreal it is without a doubt the French language connection. New Brunswick (38%) French is the primary language.
After proximity to Montreal it is the record of success (# of cups) and then as
njdevils1982 points out above the Voyaguers created huge Habs loyalty in the province with their two AHL Calder Cups here in Halifax. I know this first hand having grown up next to the forum in Halifax and our family being a billet for the Montreal Jr. Canadiens (and the Vees).
In the case of Boston people have mentioned cultural connections and that is true with many Atlantic Canadian families having worked in or having members of their families in New England. But I think the real reason is the out-pouring of aid Halifax received after the
Halifax Explosion on Dec 6, 1917. It was the
Boston Red Cross and the Massachusetts Public Safety Committee that immediately came to the aid of this shattered city before anyone did and not only provided doctors, nurses, food, etc but actually helped to rebuild the city. We still send a 40 foot tall Christmas tree each year to Boston. I have participated in that tree lighting ceremony before and Nova Scotia spends 400K on the spectacle every year (both mayor's, govt officials, concert featuring NS artists, etc). Its a GREAT show in the common every year. Atlantic Canadians'
historic relationship with New England, or the "Boston States, arguably goes back to the 18th century when first the New England Planters then the United Empire Loyalists established the first major British settlements in the region, but intensified in the late 19th century when post-Confederation economic malaise in Atlantic Canada combined with a huge demand for labour in industrial New England to create a massive shift southwards.
Boston–Halifax relations - Wikipedia
Why Nova Scotians Send A Christmas Tree To Boston Every Year
I would say for the Bruins it was also cup success in the '70's, Bobby Orr, Glen Murray, Don Sweeney and now Brad.