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The Blue Jays outrighted Martin to Triple-A Buffalo on Thursday.
Rasmussen didn't factor into the decision in Game 2 of the World Series on Saturday, giving up three runs on six hits and two walks while striking out four over 3.2 innings.
Baker issued a walk and allowed no hits in a scoreless ninth inning to earn the save in Game 5 of the ALCS at Cleveland on Sunday. He did not record a strikeout.
Peralta will start Game 6 of the ALCS against the Guardians on Monday, Marc Topkin of the Tampa Bay Times reports.
Mesa is out of the lineup for Game 5 of the ALCS against the Guardians on Sunday.
Rasmussen earned the win in Game 5 of the ALCS against the Guardians on Sunday, allowing one run on four hits with six strikeouts and one walk over seven innings.
Martinez earned the win in Game 4 of the ALCS against the Guardians on Saturday, allowing one run on two hits with three strikeouts and two walks across 5.1 innings.
Diaz went 2-for-5 with a double, a two-run homer and an additional run scored in Game 4 of the ALCS against the Guardians on Saturday.