The relationship will give you many enjoyable hours of research if you devote time to it.
It is complex but you can see the outline of it. Part of the problem is that it is hiddeen, and the actions change depending on the situation...sometimes they are tightly allied, and have common objectives on near-term matters, although their long term objectives may differ and even be opposed to each other.
For example, Hitler and Stalin best buddies early on, even after Hitler in his early days was violently anti-communist. They swore friendship and peace so they could carve up Poland. They had mutual short-and-medium term common interests, even though the public face of their philosophies were different.We all know how that friendship ended.
Sometimes these allies just use the enemy for short-term gain, figuring they can screw the other one later after the other opponents are neutralized. The global elites use radical Islam and leftist ideology as a vehicle to destabilize national governments.
They are not followers or believers of Islam themselves, for the most part; though they will promote Islam in countries they want to paralyze. And they certainly do not want to surrender their assets and wealth to the people. So they are not true socialists or communists, either.
They pick up a lot of support along the way from sincere people who believe the phony slogans and flowery rhetoric.
