CHICAGO -- Lucas Giolito and Dylan Covey talked to MLB.com this past weekend about the crosstown rivalry with the Cubs in advance of Tuesday and Wednesday night action at Wrigley Field.

At the crux of those comments made by the White Sox hurlers sat a major theme.

“Gotta beat the Cubs,” said Giolito, who starts Wednesday and has beaten pretty much everyone he’s faced this season. “That’s a big one. We are both in the same city. There’s always an added bit to that.”

“We definitely want to beat them, no doubt,” said Covey, who was a college teammate of Cubs third baseman Kris Bryant at the University of San Diego and remains close friends with him. “Every single time.”

This crosstown rivalry forever was changed by a 2005 World Series championship on the South Side and a '16 title on the North Side. Yet, facing a team one game out of first in the National League Central becomes another important measuring stick amid these 15 straight games played by the improved White Sox against playoff contenders.

But dig a little deeper, and the White Sox simply are tired of being the second team in the Second City. They understand their rebuild ramifications but are getting ready to be noticed.

“We get tired of hearing about them winning so recently, and it’s kind of the talk of the town,” Covey said.

“You got two teams in the same city, and the Cubs have been kind of the top tier team for a while now,” Giolito said. “So, I would like to see that start to shift a little bit. The only chance to really showcase that is when we do play against each other.”

Joe Maddon’s crew has earned the attention, reaching at least the National League Championship Series from 2015-17 and reaching the playoffs four straight years. The White Sox have 195 losses over the last two seasons as part of the rebuild, including a 3-7 mark vs. the Cubs.

Those fortunes soon could be changing. Although the White Sox enter at 34-36, there has been significant development shown by key rebuild components such as Giolito, Tim Anderson, Yoan Moncada, Aaron Bummer and Eloy Jimenez, who came from the Cubs to the White Sox in a 2017 trade involving Jose Quintana and will be starting his first game in left field at Wrigley.

Zack Collins, the White Sox top pick in the 2016 Draft who could see time at catcher, first base and designated hitter, will be joining the White Sox beginning Tuesday. Next season for the White Sox looms as the opening of some level of postseason contention, and if the Cubs continue their success, it gives Chicago fans pause for thought concerning an L train World Series played 10.3 miles apart.

Talk about grabbing national attention. Beating your intracity rival and winning baseball’s championship at the same time produces the ultimate bragging rights. None other than iconic White Sox broadcaster Ken "Hawk" Harrelson, who is now retired, frequently talked about Chicago’s greatest baseball decade being on the horizon.

“Hopefully that can mean in the future playing against each other in the postseason, which would be really cool. That would be great. That would be sick,” Giolito said. “For now, we have the series coming up, and I’m looking forward to it. I think the rivalry is a ton of fun.”

“It would be great for baseball, and it would be great for the city,” said White Sox manager Rick Renteria, who has managed both Chicago teams. “It would be awesome.”