Dragon: Sakazuki is kind of infatuated with Dragon. The only reason he pursued to finish off Luffy in Marineford was the very fact that he was Monkey D. Dragon’s son though you can argue that Luffy’s gust of King’s Haki played a role, regardless being Dragon’s son played the most significant role in his judgment. This only intimates that they have a history though we are in a total dark regarding the possible contentions between them, but who knows Dragon may have betrayed Marines/World Government while pretending faithful to Sakazuki the whole time and it may have scared him to such extent that he began to loathe Dragon to his very core.
Blackbeard: He is a very ambitious man and in order to establish his clout in the One Piece world he has to show some kind of exploitation. Though he got to the epithet of Yonko after beating remnants of Whitebeard pirates including all the commanders except for Ace, but that doesn’t tantamount to the league of other Yonkos. Whitebeard was the lone wolf of his crew. Compared to other right-hand men of other Yonkos, Whitebeard’s right hand man, if he had any- Marco, is inferior. Someone inferred that Kaido was the righthand man of former Whitebeard crew and that is why he is so much attached to Whitebeard. So no way Marco is on par with Ben Beckmann or other right hand men of the Yonko except for Blackbeard crew. Moreover, when Shanks met Whitebeard he talked to Marco as if he was not that much familiar with him, he said: “you are first division commander Marco, aren’t you? Will you join my crew?” If Marco was with Whitebeard for a long time Shanks wouldn’t have talked like that, moreover, it could be Marco was not that strong but when he found Phoenix Devil Fruit he gradually became strong, and Whitebeard took him in from a difficult situation and let him stay in his Mobydick and we have Ace’s flashback of this scenario when Ace asked him that why they call Whitebeard as Oldman?
Anyway, Blackbeard have to show some exploit to the world in order to let the people think that he is more of a big shot than his current status and invading Baltigo was the fruition of that thought. In in the end he is gonna challenge Marine and Akainu. When he was fleeing to the New World with his newly recruited crew, he saw Akainu coming but he didn’t go for a clash even though he had the entire crew with him though he was showing off in Marinford and proclaiming himself as the strongest man alive; when he saw Akainu he said: “we are not ready yet to fight him,” Which means he has planed to fight him eventually.
Sabo: Ace fought Akainu for Whitebeard’s honor and eventually sacrificed his life for his little brother- Luffy. Sabo could fight Akainu in order to save Luffy, however, this time he wouldn’t die though he could get injured and they could both be injured, and with this fight he would avenge Ace by saying: “You logia Devil Fruit user suck a Haki, just because you have a superior Devil Fruit you get cocky,” and finally dealing a very deadly blow. Though after the fight Akainu will get recuperated soon due to some hax technology or from a potent healer.
Luffy: After defeating Blackbeard and attaining One Piece, Luffy will declare war on the World Government which Whitebeard predicted and of what the World Government was scared. In this fight Luffy will fight Akainu to settle the score of the Marineford and defeat him and injure him to the point where Akainu would get severely injured to point of paralysis.
*Theory by Samara Jordan