Doug Weight gave his players Monday off following an emotional week. Jack Capuano was fired on Tuesday, Weight replaced the longtime coach and the Islanders played three games in four nights, culminating in Sunday’s 3-2 overtime loss to the Flyers.

The Islanders’ 3-0-1 week has helped them get to the fringe of the Eastern Conference playoff race, but the real tests are still to come: The next three games are against the Blue Jackets, Canadiens and Capitals, three of the top four teams in the East, with Columbus coming to Barclays Center on Tuesday for its first visit of the season.

“They’ll get their rest, rest their minds a bit, but we also have to watch the video and see what we’ve done,” Weight said after Sunday’s loss, a game in which the Islanders held a 2-0 lead and brought a 2-1 advantage into the third. “They also need to see the things they did well.”

As they did on Saturday against the Kings, the Islanders gave back a 2-0 lead early in the third and rebounded with a stronger effort after their opponent tied it. Against the Flyers, the Islanders had two power plays in the third after the game was 2-2 and came close to regaining the lead as they did in Saturday’s 4-2 win.

But the result was another point lost that left the Islanders in a three-way tie for 14th in the East, five points away from the last playoff spot. And it’s the Flyers who sit in that second wild-card position, another small dagger to the Islanders, who are 4-6-3 in the Metro Division and 9-12-3 in the East.

“We’ve shown some progress the last few weeks,” Alan Quine said after Sunday’s loss. “We’re playing more the way we want to be playing.”

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Whether that can translate into a genuine run out of the Eastern Conference depths hangs on games like Tuesday’s, against John Tortorella’s remarkable Blue Jackets.

Notes & quotes: Andrew Ladd was one of a handful of Islanders who skated on Monday while the rest of the team was off and Ladd, out the last four games with an upper-body injury, could return Tuesday. Travis Hamonic (knee) also skated, his first time on the ice since Jan. 8, but it will be some time before his return . . . Thomas Greiss was named the NHL’s second star of the week after posting back-to-back shutouts.