Murray, 26, and already with two Stanley Cups on his resume, went 20-11-5 with a 2.87 GAA and .899 save percentage in 38 games.
The intense competition to play will push both of them to be better, and both Sullivan and Jarry said the friendship between the goalies benefits both.
"The best possible scenario is when guys sincerely like one another and friendships are built," Sullivan said. "Those positive relationships help both guys. I believe we have that with Matt and Tristan. They're two guys who came through Wilkes-Barre together and are now in Pittsburgh together. They push each other to be the best. They're competitive guys, and they both want the net."
"It's awesome we have the relationship we do," Jarry said, "and it's awesome we're able to push each other. It's a good, healthy relationship.
"Right now, we're just trying to get back in shape as quick as we can, get ready to play and get ready for that first exhibition game."
The final decision on who will start in goal is up to Sullivan and goaltending coach Mike Buckley - it's a pleasant problem to have - but you can rest assured that Diesel and Kitty are pulling for Jarry.