The first time Danielle Ezzo met Matt and Rachel, she was relieved. The fashionable trio had met on the dating site, Nerve, and had been exchanging messages, but hadn’t yet met in real life. Ezzo, 29, recalls that evening at the Bowery Hotel in spring 2009 fondly: “I was excited that they were just as cute as their profile pictures.”

She was even happier to learn that she had that hard-to-find thing with both Matt and Rachel — chemistry. They talked about life and love and learned that they had the same ideas when it came to dating.

“I was really excited to meet people that felt the same way,” she says of her ongoing relationship with the married couple, both 34-year-old self-employed artists, who declined to use their last names because of privacy reasons.

Ezzo, also an artist, is polyamorous. Loosely speaking, she seriously dates more than one person at a time, and has an emotional, as well as a sexual connection, with her partners.

She sees Matt and Rachel separately and together, and also occasionally dates other people.

“One of the wonderful aspects of polyamory is that you do get different things from different partners, both emotionally and physically,” says Ezzo, who is in what’s known as a “triad” with Matt and Rachel.

“There are three very different dynamics, all of which are personally valuable.”

And while the arrangement may seem unusual, Ezzo insists it’s really no different than run-of-the-mill monogamy. Communication and compromise are key — for instance, when it comes to picking a flick to watch for the evening.

“They have very different styles in movies,” says Ezzo, who splits her time between New York and Boston, where she is going to school for photography at the Art Institute of Boston. “When I’m with Rachel we might [watch] a silly, fun ’80s movie, but I won’t do that silly ’80s movie with Matt. He likes strange horror flicks.”

Luckily, she says, “I like both of those things.”

Ezzo is part of a growing movement of people who are practicing consensual non-monogamy — or, in plain English, open relationships.

According to Gette Levy of Open Love NY, a local support group with more than 1,000 members, the organization has seen a steady increase in membership since forming in 2009.

“Dating has changed over the past 50 years,” says Levy. “Many adults of all ages are finding that monogamy does not suit them and is no longer a fiscal and social requirement.”

Shortly after she started seeing Matt and Rachel, Ezzo met her future husband.

“I had told him [about my lifestyle] on our first date,” she says. “He was excited to explore it.”

Her open marriage eventually fizzled for reasons not related to polyamory, but her relationship with Matt and Rachel is still going strong.

“I’ve always inherently had this notion of or had this blurred line between friendship and lovers … to me there is a huge overlap. It’s easier for me to simultaneously love multiple people,” says Ezzo.

“As a bi-sexual person, choosing is not necessarily something that I personally like to do,” she adds.

Pop-culture is having a poly moment too: TV shows like “Sister Wives” (Sundays on TLC) and “Polyamory: Married & Dating” (Thursdays on Showtime) are giving people a glimpse into the complicated sex lives of multi-partnered couples.

“The interest and the visibility around open relationships has just skyrocketed,” says sexpert Tristan Taormino, who wrote a book about the subject, “Opening Up: A Guide to Creating and Sustaining Open Relationships.”

“We’re having these discussions in really mainstream media that just weren’t even possible two years ago,” adds Taormino, who points out that her book actually sold more copies last year than it did during its 2008 debut.

Open relationships are becoming so common that when singer Robin Thicke gripped Lana Scolaro’s barely covered butt at a VMA afterparty at 1OAK last month, his indiscretion reportedly didn’t get him into trouble with his actress wife Paula Patton.

“We’ve done just about everything,” Thicke said of his unconventional relationship to Howard Stern in July. Still, he stopped short of saying he and his wife were in an open marriage: “Out of respect for her, we just won’t answer that one.”

Will and Jada Smith, Mo’Nique, Tilda Swinton and even Dolly Parton and her husband have all been rumored to be in open relationships too.

But perhaps the lifestyle’s most visible celebrity moment came in January 2012, when Marianne Gingrich told ABC News that her ex-husband, the politician Newt Gingrich, had asked for an “open marriage” while having an affair with his soon-to-be third wife Callista. (Newt Gingrich has given several extensive denials regarding his ex-wife’s claims.)

It’s not just horny men with insecure wives looking the other way who are in non-monogamous relationships — often, women are the ones who instigate the practice.

Several studies by sex researchers in Germany and in the University of Wisconsin have shown that it is often women who become bored romantically after several years in a monogamous relationship.

Violet, a New York City higher education teacher, 49, would only speak to The Post under a pseudonym. (She says her friends know about her life style but some of her adult students might be shocked.)

“The way I describe it on my OKCupid profile is about the best I can do: I just didn’t get the memo about not dating,” she says.

Violet’s love life is the stuff of telenovelas: She has been in a marriage with a man for 10 years. Her husband has a girlfriend of three years. Violet is also dating a man and a woman who date each other but, unlike Ezzo, she only sees each person in the couple separately, never together. And she goes on dates outside of her regular relationships.

In a twist, her husband’s family knows about his girlfriend and the trio often go to family functions together.

Violet focuses on her two other partners when her husband is traveling; when he is home, “I will usually spend maybe one or two nights with somebody else.” Her husband’s long-term girlfriend lives out of state, she explains, so he’ll go spend a week with her at a time.

“It all comes out in the wash,” she says.

Violet, for whom sex is a “big priority,” prefers three lovers because the arrangement “keeps me from becoming a burden on any single one of them.”

“There is crazy, wild sex and lots of it, and that’s important to me, but it’s not all there is to my love affairs — not by a long shot,” says Violet.

Unexpectedly, the biggest difficulty people in non-monogamous relationships encounter isn’t jealousy, but something way less dramatic.

“Time is the real thing,” says Taormino, who is in an open marriage herself.

Ezzo’s partner Matt agrees: “The biggest misconception people have about open relationships is that it’s a nonstop party. We only have 24 hours in a day and most of that is taken up with work, sleep and responsibilities to the home and each other. To see someone else takes a lot of planning. We live by the calendar more than the bedroom.”

Another misconception? That there are no rules.

But when an open relationship involves long-term emotional connections with multiple partners, there are frequently more, not fewer, rules.

The marriage contract of the San Diego family featured in “Polyamory: Married & Dating” is nearly five pages long. Posted online, it has extremely specific codes of conduct ranging from when to talk about relationship problems (“No relationship processing after 9:30.”) to guidelines around dates (“Do not postpone or cancel a date with one partner to see someone else.”).

Even with all the complications of having multiple relationships, proponents believe it’s better than the alternative.

“I feel like monogamy sets us up to fail in so many ways….that this one person is going to meet all of our needs — emotional, sexual, physical, spiritual, financial, physical — and that’s impossible,” says Taormino.

“I think polyamorous people acknowledge that up front.”

Violet agrees — and counsels her female friends who are going through the trials of dating in New York to be more open-minded.

“They would go on a first date and they would hold some guy up to this ridiculous standard and I would tell them, ‘Look, just have fun. Date a bunch of people. Don’t have these expectations.’ ”

Looking to break free of monotonous monogamy?

Here’s a key to some of the most popular open-relationship styles. And remember, all are consensual — cheating is not kosher!

Open relationship: Umbrella term for any consensual non-monogamous relationship

Polygamy: Think “Big Love.” One spouse, many wives. Illegal.

Monogamish: Don’t-ask-don’t-tell sanctioned cheating in a monogamous relationship

Polyamory: Having a loving relationship — emotional and physical — with multiple people

Swinging: Hook-ups with no-strings attached