Connectivity between core networks from different vendors

I am from academics and hence have less knowledge about actual deployment.
My question is that what is the interface between core networks of different vendors. For example, a Vodaphone UE(V-UE) is connected to a Vodaphone Core network (V-CN), and a Reliance UE (R-UE) is connected to a Reliance Core network (R-CN). Now if the V-UE makes a connection with R-UE, I believe that the V-CN and R-CN communicate with each other. So what is the protocol of this communication and what is the interface?
Best regards

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