According to many anthropologists a land brigade during the ice age allowing between which two countries

Continents: North America and Asia
Countries: Canada and Siberia, or Alaska (United States) and Siberia

Well first of all, I think you're referring to the theory of the land "bridge",
not 'brigade'.

The main problem with this question is that during the Ice Age,
there were no countries, so there are no names to answer with.

The suspected land bridge spanned the expanse of open water
that would come to be called the 'Bering Strait' millions of years
later, after the bridge was long gone.  Its ends would have been
located on land in different parts of what would come to be known
as Mother Russia far in the future.  And even later, after another 
couple hundred years, one of those ends would cease to be part
of Russia and would become part of the USA.  But as I said earlier,
during the time that the land bridge existed, there were no countries.