How Geiger Murder and Sean Reagan Murder related to each other?

Question

In The Big Sleep (1946), Philip Marlowe was hired by General Sternwood to get rid of Arthur Gwynn Geiger’s blackmail. Later Geiger was found killed somehow. After knowing that the case is closed, Philip Marlowe was paid $500.

But Philip Marlowe becomes busy again solving whereabouts of Sean Regan who is later found killed by Eddie Mars.

But how are these two murder cases related?

Why I got doubt is: After the first case is over, Vivian paid money to Philip Marlowe, during that time Philip Marlowe mentions Eddie Mars’ name in front of her. She started shaking before him.

“Oh, come now, angel, stop shaking.”

Answer 1

It’s complicated especially as Raymond Chandler wasn’t quite clear on everyone’s motivations or, indeed, who killed who.

The Big Sleep is known for its convoluted plot. During filming, allegedly neither the director nor the screenwriters knew whether chauffeur Owen Taylor was murdered or had killed himself. They sent a cable to Chandler, who told a friend in a later letter: “They sent me a wire … asking me, and dammit I didn't know either.”

^Wikipedia

But… essentially, Carmen Sternwood killed Sean Regan and Eddie Mars / Arthur Gwynn Geiger were blackmailing her (or the Sternwoods) over it.

This is a little clearer in the novel as explained by the Wikipedia entry…where Sean Regan is called Rusty.

Carmen came on to Rusty [Regan] and he spurned her, so she killed him. Eddie Mars, who had been backing Geiger, helped Vivian conceal it by first helping to dispose of Rusty's body, inventing a story about his wife running off with Rusty and then blackmailing her himself. Vivian says she did it to keep it all from her father so he wouldn't despise his own daughters, and promises to have Carmen institutionalized.