Why does Antony befriend Brutus, Cassius, and the other conspirators?

After Caesar is assassinated, Antony flees to his own home. But he must realize that he has no safety anywhere in Rome if the conspirators decide to kill him too. He sends a servant to meet with Brutus and deliver a verbal message which includes the following.

If Brutus will vouchsafe that Antony
May safely come to him and be resolved
How Caesar hath deserved to lie in death,
Mark Antony shall not love Caesar dead
So well as Brutus living, but will follow
The fortunes and affairs of noble Brutus
Thorough the hazards of this untrod state
With all true faith.     (III.1)

Antony addresses Brutus as the leader of the faction. He knows that Brutus will be easier to manipulate than any of the others. Brutus is a man of honor, and as such he tends to believe that other men are like himself. He believes everything Antony tells him. Antony shows precisely what he is afraid of, and why he is using all his cunning to save his own life, when he says:

I know not, gentlemen, what you intend,
Who else must be let blood, who else is rank.
If I myself, there is no hour so fit
As Caesar's death's hour, nor no instrument
Of half that worth as those your swords, made rich
With the most noble blood of all this world.    (III.1)

The reason Antony fled to his home in the first place was that he expected a general blood-letting after the assassination. And Antony knew he would be the man most likely to be murdered next. That is what would have happened if Cassius had had his way. Cassius is a cunning, deceitful man and judges Antony by himself, just as Brutus judges Antony by himself. But Brutus has taken over the conspiracy because of his great reputation. If Brutus had not let himself be tricked by Antony, the conspirators would have formed a new government and Antony would have been lucky to save his own life and flee from Rome. Instead, Antony turns the tables on Brutus, Cassius, and the others and forms a triumvirate with Octavius and Lepidus. These three men initiate a massacre of Roman senators and others after the mutiny aroused by Antony in his funeral speech forces the conspirators to flee from Rome.

Antony makes friends with the conspirators conditionally. Brutus must "be resolved / How Caesar hath deserved to lie in death..." This is a cunning ploy. Brutus welcomes the opportunity to show off his oratorical powers, and he has thought about all his reasons for leading the assassination plot. He is so eager to defend his virtue in his funeral speech that he doesn't think about what Antony might say if he permits him to make a funeral address of his own. Cassius, however, is not so easily fooled. He tells Brutus:

You know not what you do. Do not consent
That Antony speak in his funeral.
Know you not how much the people may be moved
By that which he shall utter?      (III.1)