The relationships between A and B and C
Let's say there're two sets of studies: one looking at the relationship between physical exercise and depression and the other between smoking and depression.
If I want to summarize this in one sentence, is it correct to say "There are studies looking at the relationships between physical exercise and smoking and depression.

Question

Answer

There is a study on the relation between physical exercise and depression while another looks at smoking and depression.

Answer

That's a good question; as native speakers, we risk ambiguity when writing such sentences ourselves. Your sentence indicates that there are more than one study which investigates the links between three factors, and this is not what you meant.  Your first sentence which explained the problem was good and you did not need to rewrite it.

Answer

Some options:

1)There are studies looking at the relation between depression and both physical exercises and smoking.

2)There are studies looking at the relation between depression and physical exercises and between depression and smoking habit.

3) There are studies looking at how depression relates to physical exercises and smoking.

I hope I've helped!