I don't believe that Shanks vs. Kaido was a long battle. They clashed, then either (1) Kaido was incapacitated or (2) he noticed that he wouldn't be able to go after Whitebeard, then he retreated (remember that only King was alongside him, so he was at a great disadvantage).
Chronology of the events (IMO): (1) Whitebeard left his territory to save Ace in Marineford > (2) Kaido heard the news and went after Whitebeard > (3) Shanks intercepted Kaido and they clashed (was he keeping tabs on WB?) > (4) Whitebeard continued and arrived in Marineford > (5) Shanks repelled Kaido and followed Whitebeard > (6) Shanks arrived in Marineford long after the war had started.
Chronology of the events (IMO): (1) Whitebeard left his territory to save Ace in Marineford > (2) Kaido heard the news and went after Whitebeard > (3) Shanks intercepted Kaido and they clashed (was he keeping tabs on WB?) > (4) Whitebeard continued and arrived in Marineford > (5) Shanks repelled Kaido and followed Whitebeard > (6) Shanks arrived in Marineford long after the war had started.
op is really worst than fairy tail