Describe the relations among the triumvirate?
The relationship is based on convenience. Antony explains to Octavius that Lepidus is "a slight, unmeritable man" of few ideas, and what ideas he has are second-hand and out-of-date. He will carry loads, and then, when he has served his purpose, be put out to pasture - rather like Antony's horse.
Then, in Act V, Antony's authority is challenged by the young Octavius, when he confronts Antony over who will command the right flank of the army. Octavius calmly asserts his will: "I do not cross you; but I will." (V.i.20)
Compare this to the relationship between Brutus and Cassius, the two leaders of the conspiracy. How do these two men feel about each other? Is political or expediency stronger than affection?
The second triumvirate, much like the first, had two major players and a third tag-a-long. In the second, Anthony and Octavious discuss the merit of Lepidus. Octavious seems to prefer keeping Lepidus because he's earned his spot as a tried and true soldier; Anthony counters by saying his horse is also battle tested and for that earns his meal and nothing more. Anthony really does not want to split the Roman world three ways and feels Lepidus is the weakest link.
This is very similar to the relationship of the first triumvirate containing Caesar, Pompey, and Crassus. Crassus was disposed of quickly leaving Caesar and Pompey to battle for sole leadership.