The portion over Canada is not designated US Class B but Canadian Class C.
Note that Canadian Class C airspace definition is similar to US Class B. In particular, VFR aircraft must obtain clearance prior to entry. A mode C transponder is required.
To add: airspace over Canada is generally managed by NAV CANADA. Definition for the Canadian side of the Detroit Terminal Control Area (TCA) can be found in NAV CANADA's Designated Airspace Handbook, portions excerpted below (from page 78):
We can see that these definitions matches the eastern portions of the Detroit TCA exactly, e.g, the outer area altitudes from 6,000' to 10,000' bounded 30nm from the Detroit VOR (DXO).
The Detroit TCA airspace was modified a few years ago, which required coordination between the FAA and Nav Canada. The following discussion from the US Federal Register (page 3307) may be of further interest:
Also, as noted in the NPRM, the
eastern portion of the DTW Class B
airspace area extends into Canadian
airspace. The equivalent Canadian
airspace to Class B airspace, as
designated in the United States, is Class
C airspace. NAV CANADA, the
Canadian air service navigation
provider, generally designates Class C
airspace with a 12,500 feet MSL ceiling,
however, has advised the FAA of its
willingness to establish corresponding
Canadian Class C airspace adjoining the
FAA’s DTW Class B airspace with a
ceiling of 10,000 feet MSL.
Additionally, NAV CANADA advised it
would make the Canadian Class C
airspace action effective to match the
effective date of this DTW Class B
airspace modification action.