The filter size for the 60-600 is 105mm. 
The 82mm for the 70-200 is a first but all the modern 16-35/24-70 lenses already have this size anyway, so it makes sense to have a common filter size - only 82mm instead of 77mm.
The 82mm for the 70-200 is a first but all the modern 16-35/24-70 lenses already have this size anyway, so it makes sense to have a common filter size - only 82mm instead of 77mm.