Which is why it has been fascinating to listen in as Bob Neumeier deftly navigates the stormy sports radio showdown between WEEI and The Sports Hub . . . by somehow working for both sides.

“I kind of have felt like a double agent,’’ laughed Neumeier, who has filled in as a co-host on both stations over the past two months and is currently providing WEEI listeners with a pleasant reprieve from the usual bitter fare in the mornings, cohosting “The Dennis and Callahan Show’’ with the Globe’s Bob Ryan. “I’m working for the Americans, the Germans, the Russians all at once. I’ve sort of been waiting for someone to say, ‘You can’t do this anymore.’ ’’

Neumeier most recently filled in on The Sports Hub during the NBA Finals in June, and his radio duties are exclusive to WEEI over the next couple of weeks. He also recently made his debut as a co-host on WEEI’s drive-time program “The Big Show,’’ and according to a source with knowledge of the situation, he has drawn significant interest from Comcast SportsNet New England for an expanded role after a one-night stint as a co-host of “SportsNet Central.’’

Though he hasn’t held a full-time gig in the area since walking away from WEEI in a disagreement over salary early in 2005, Neumeier remains a well-known personality in Boston and beyond, and his résumé is impressive.

He was the radio voice of the Hartford Whalers in the late ’70s and of the Bruins for four seasons in the late ’90s; he spent 20 years as a sports anchor and reporter at Channel 4; he covered three Olympics for NBC, and still contributes to the network as a horse racing analyst. (After his departure from WEEI, he worked for 3 1/2 years at NBC, but his contract was not renewed in September 2009. Said Neumeier, “That was a situation that disappointed me a great deal, but that’s how the business goes.’’)

Neumeier’s appeal — to potential employers as well as listeners, who according to my e-mail inbox generally seem to appreciate his bemused tone and occasionally meandering style — isn’t due solely to his recognizable name or his list of achievements. It’s also due to some remarkably useful personality traits for the business he is in: a thick skin, a refusal to burn bridges, and a habit of favoring common sense over ego.

With a more jaded or emotional perspective, it’s hard to believe a reunion with WEEI would have been possible given his departure in 2005.

“I came to an impasse with them as to a contract, and basically we shook hands, agreed to disagree, and I walked away from a job because I wasn’t satisfied with their offer,’’ Neumeier said. “No hard feelings. Sometimes that stuff happens.

“I just wasn’t happy with what they were offering me, I gave them an ultimatum, they gave me theirs, and we walked away. To be honest, it wasn’t even close. But I knew it even then: It’s a waste of time and pretty foolish to be bitter.

“The fact that they’ve welcomed me back is proof-positive that apparently they didn’t throw me in the coffin and bang down the nails. My attitude about it was I’ve never seen any reason to make enemies. It doesn’t make sense politically, it’s not good businesswise, it’s not good for my mental health. It’s just not part of my being.’’

Neumeier, who spent much of his time in Miami after leaving WEEI five years ago, said he is back in Boston more often these days after getting married a day after Christmas to a woman who works full-time here. His personal circumstances have changed, and he has long realized the same will often be true in his professional life.

“That’s the media world. It changes from day to day,’’ Neumeier said. “Opportunities that seem closed to you are suddenly open, and as long as you conduct yourself in a professional manner, show up on time, and try to do a good job, you always think there will be something there for you. That’s always been my philosophy, and it’s served me well.’’