MEXICO CITY — At the foot of Mirna Cano Cozar’s mattress on the gymnasium floor, volunteers circled young children for a singalong, and then held a session of drawing with crayons.

At this public rec center, one of dozens of makeshift shelters for earthquake victims, Cano, a music teacher, has access to day care for her two daughters, veterinary services, group and individual psychological counseling, showers, vaccines and a row of stationary bikes. Outside, volunteers have piled blankets and cans of food, and gallon after gallon of water.

Maybe the only thing this shelter lacks is a lot of people like Cano.

Here at the most populated relief shelter in Mexico City, according to city staff who run it, 460 people have registered, although there is space for 800. During a visit Friday, two television crews (and this reporter) found the gym only sparsely filled. While Cano is grateful for the care she has received, her worries are longer-term: when will the city inspect her damaged apartment; how will she find a new place to live; how can she relax enough to stop sleeping with boots on, for running in case of another temblor.

“We want help but not food or money,” said Cano, 42. “We want a life. We want to regain our freedom.”

Exclusive footage shows the Topos (Spanish for moles), a volunteer search and rescue team, searching for survivors after the earthquake in Mexico City. (The Washington Post)

The outpouring of aid in Mexico City since Tuesday’s deadly temblor has been inspiring. Restaurants have offered free food; brigades of volunteers with hard hats and shovels have dug into rubble; people have given up their spare rooms for friends and relatives flushed out of homes by the disaster.

At the same time, many here sense that the donations may not be targeting the needs of the victims. The focus has been on first aid — water, food, medicine — while more people appear to need services such as building inspections or architectural work. In Mexico City, power is back for the vast majority of people; many stores and restaurants are open.

“What we’re hearing right now is that Mexico City is pretty much, for the moment, covered,” said Melissa Martinez, who started a volunteer relief group (Voluntarios@JuntosSismoCDMX on Facebook and Twitter) to help divert aid to places that need it.

“The shelters that were set up were mostly empty,” said Martinez, who is a professor of migration studies in Mexico City. “People who were affected, most of them stayed with friends.”

The priority now, she said, is to collect building materials and plan for reconstruction in places such as Morelos. That state south of Mexico City suffered at least 73 fatalities in the quake, second only to Mexico City, with 155. In total, at least 293 people died in the disaster.

Many people attribute the disjointed nature of the response to social networks and media coverage that fixated on the images of destruction, creating a war-zone perception about Mexico City, when in reality many parts of the capital are functional.

Where Mexico's earthquakes have struck

The televised saga of “Frida Sofia,” the supposed 12-year-old girl trapped in the rubble of her school in southern Mexico City, was one example of the misperceptions that emerged in the wake of the disaster. The effort to rescue her riveted the nation, fed by round-the-clock TV coverage, but then took a bizarre turn on Thursday when authorities concluded that Frida Sofia didn’t actually exist. Some people faulted the Mexican navy for spreading bad information and others blamed Televisa, a prominent network often accused of being cozy with the government, saying it fed the media spectacle and showered officials leading the rescue with attention.

But some felt that the “Frida Sofia” story was not so much about willful deception as about what can happen after a disaster when there is intense pressure to help victims, and a chaotic rumor mill involving hundreds of volunteers.

As Gabriel Stargardter, a Reuters reporter in Mexico City, wrote on Twitter: “We’re all to blame, because we all wanted her to exist. .”

Magazine editor Esteban Illades said social media had proven to be a double-edged sword, perpetuating false stories such as the Frida Sofia case, but also spreading accurate information quickly.

“Within just a few hours, people learned how to spread the message and channel help,” he said.

Mexico, with its history of devastating earthquakes, including the 1985 temblor that left thousands dead, has been drilling for disasters for decades, and thousands jumped into action as soon as the shaking stopped on Tuesday.

“My generation has lived with that our whole life,” said Hector Castillo, a sociologist at the National Autonomous University of Mexico. “And we have transmitted that to the younger generations. ”

Andres Barrios, who runs a venture capital firm, was one of many citizens who rushed to help after the quake, organizing motorcycle teams to run supplies throughout Mexico City. Working with other volunteers in a Red Cross office, he gained an appreciation of how the city government was using its network of cameras and local intelligence to help distribute aid.

“Everybody thought it was a complete mess …[but] they were actually making an intelligent deployment of the people and the volunteers,” he said.

Some, however, felt the government needs to improve its ability to coordinate and communicate.

“It seems to me that this is not so much overreaction by society, but that the authorities have a limited capacity for reacting and channeling this social energy,” said Saul Arellano, director of the magazine Mexico Social.

Across the city, volunteers who manned support sites said that while they appreciated the generosity, managing the overflow of supplies had become a problem in itself.

“We’ve got enough food and water, for example, but people keep arriving with more, it’s hard to store everything,” said Jimena Carrasco, a student and volunteer at a drop-off point in the central Roma neighborhood.

“Meanwhile, there are other sites where they are still requesting stuff,” she said.

Many Mexicans have been eager to help in any way possible. Upon hearing that a shelter had been set up to take care of animals, one 32-year-old resident, who identified himself only as Alberto, filled his shopping cart full of dog food on Wednesday.

“What can I say? I’m an animal guy,” he said in the supermarket. “It seemed the right thing to do.”

Gabriela Martinez in Mexico City contributed to this report.