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> taking over Italian East Africa, [...] and nearly defeating Italian positions in Libya. [...] As a result the possibilities of integrating the colonial empires of Germany’s vassals [...] were blocked.
But by Tooze's measurement, overseas lands were worthless anyway. Even Europeans couldn't add much to the war machines of the Axis. However these:
> suppressing pro-Axis governments in Persia and Iraq
> connecting with Japan through South Asia were blocked
were more important in this question.
Even if the Germans could acquired the Sovier Caucasus, they would have to defend it against the Brits from the south (whom could approach from the Levant and India).