Puk (elbow) is expected to begin a throwing program in the coming week, Alex Weiner of ArizonaSports.com reports.

Puk was placed on the 15-day injured list April 19 with left elbow inflammation before later being transferred to the 60-day IL on May 1. The left-hander isn't eligible to be activated for over a month, but beginning a throwing program will be the first step in his build up to returning to action down the road this season.

Martinez (shoulder) will throw to live hitters Wednesday, Alex Weiner of ArizonaSports.com reports.

Martinez felt strong after completing a bullpen session Sunday, and it's another positive sign that he's progressing to throwing against hitters Wednesday. It remains unclear if the D-Backs will send the 23-year-old out on a rehab assignment, as he'll be eligible to be activated from the 15-day injured list Friday after going down with shoulder inflammation at the beginning of the month.

The Diamondbacks designated Castillo for assignment Monday.

Castillo will lose his spot in the Arizona bullpen with the Diamondbacks activating right-hander Kendall Graveman (back) from the 15-day injured list in a corresponding move. After getting called up from Triple-A Reno on May 1, Castillo filled a low-leverage relief role and gave up eight earned runs on 10 hits and three walks in 6.1 innings across five appearances. The 29-year-old lefty is likely to clear waivers and will have the option of either accepting an outright assignment to Reno or electing free agency.

The Diamondbacks reinstated Graveman (back) from the 15-day injured list Monday.

Arizona designated lefty Jose Castillo for assignment to open up a spot in the bullpen for Graveman, who missed the first month and a half of the season while recovering from a right lumbar strain. Graveman had previously missed the entire 2024 campaign while on the mend from right shoulder surgery, but he checked out healthy after tossing 3.1 scoreless innings across his three minor-league rehab appearances. Prior to his shoulder surgery, Graveman found success as a setup man and occasional stopgap option at closer, but he may have to settle for a middle-relief role initially with Arizona coming off a lengthy absence from big-league action. The back end of the Diamondbacks bullpen is highly unsettled, however, so Graveman could move up in the pecking order quickly if he excels in his first few relief appearances.

The Cubs optioned Hollowell to Triple-A Iowa on Monday.

He'll cede his spot on the 26-man active roster and in the bullpen to left-hander Caleb Thielbar (personal), who was reinstated from the paternity list. Hollowell has fared well over his five appearances for the Cubs between his two separate stints in the big leagues this season, giving up just one earned run and striking out five batters across 6.1 innings.

The Cubs reinstated Thielbar (personal) from the paternity list Monday, Jared Wyllys of AllCHGO.com reports.

Thielbar was away from the Cubs for the maximum three games while he welcomed a new addition to his family. Chicago optioned righty Gavin Hollowell to Triple-A Iowa to clear a spot on the 26-man active roster and in the bullpen for Thielbar.

Otanez (shoulder) struck out three and allowed two hits and no walks over two scoreless innings in his rehab appearance Sunday with Triple-A Las Vegas.

Otanez has been on the shelf all season due to a right shoulder sprain, but he appears to be on the cusp of a return from the 15-day injured list. After he was briefly shut down following an April 26 rehab appearance with Single-A Stockton, Otanez headed to Las Vegas earlier this month and has made four appearances for the Triple-A club over the past week. Otanez is likely to fill a middle-relief role for the Athletics once activated.

McFarland (groin) is scheduled to undergo an MRI on Monday, MLB.com reports.

McFarland sustained a left groin injury while covering first base on an Austin Wells groundout in Sunday's 12-2 loss to the Yankees. The MRI should shed light on the extent of the groin issue and will likely determine whether McFarland requires a stint on the injured list. The veteran southpaw reliever has notched five holds and has turned in a 5.23 ERA and 1.74 WHIP over 18 appearances with the Athletics this season.

Miller was charged with a blown save in Sunday's 7-6 extra-inning loss to the Twins, allowing two earned runs on three hits and one walk without retiring a batter.

Miller entered the game in the sixth inning with a 4-3 lead and was tagged with his second blown save of the season after a lackluster performance. The left-hander surrendered three singles and threw just six of his 12 pitches for strikes before being pulled. Miller now owns a 2.19 ERA, 1.70 WHIP and an 11:9 K:BB across 12.1 innings in 15 appearances.

Stanek (1-3) struck out two in a perfect eighth inning Sunday to pick up the win over the Cubs.

With the score tied 2-2, the right-hander breezed through Chicago's 9-1-2 hitters on 11 pitches (eight strikes) before the Mets' offense erupted for four runs in the bottom of the frame. After a rough end to the month of April that included three straight losses and blown saves, Stanek has yet to allow a run in May, posting a 5:0 K:BB over five scoreless innings as he re-establishes himself as a reliable high-leverage option for the Mets.