Lesbos, Greece (CNN) The cemetery on the Greek island of Lesbos is small. It has ancient cypress and olive trees, marble mausoleums and angels carved from alabaster. There also are more than 120 dirt graves marked only with chunks of broken marble.

These are the people who died on the crossing to Europe.

Christos Mavrahilis is the garrulous caretaker here -- 54 years old, he spent a life at sea before deciding to settle down here seven years ago.

"I don't care what religion people are," he says. "Christian, Muslim or Buddhist. We are all flesh and bone.

"When our bodies go silent, we are returned to the earth."

He shows us the graves that now run up against the cemetery walls. Most are labeled "Unknown" with a date of death. Some markers have the coroner's file numbers painted on where families can find DNA and other information that may help to identify the dead.

One grave is also marked "Plomari Beach" -- where the body was found.

Another simply says "Afghan" with a date.

The grave of 1-year-old Safi Siyap, who drowned while the coast guard attempted to rescue her family.

'Little angel'

Mavrahilis has his own way of remembering those buried here.

He is drawn to the grave of a 1-year-old child marked "Safi Siyap" but he calls her "the little angel." The parents were in a boat picked up by the Greek coast guard in rough seas, he said, but as they tried to hand her over to safety, the child fell through their arms and drowned.

The names of two Iraqi sisters, a 2-year-old and a 7-year-old, are engraved on a simple marble slab.

He remembers the distraught parents burying the girls then continuing on their journey north through Europe.

"Life must go on," Mavrahilis tells us.

But the cemetery has now run out of space. The caretaker says he has had to exhume and rebury bodies to make space for more.

Bodies stacking up

Mustafa Dawa has just turned 30 years old. Though he is an Egyptian student of Greek literature, he has spent the last year in Lesbos as a volunteer and now dedicates himself to providing Muslim burial rites to asylum seekers.

"By October, there were 70 bodies in the morgue waiting to be buried," he tells CNN.

Mustafa Dawa digs graves but also conducts Muslim burial rites for refugees who failed to make the crossing.

"They were there for 38 days. I know because I went to the hospital to help a man identify his sister but when I went into the morgue, I saw 45 bodies piled up on top of each other. Men and women. Some of them naked. I was so angry and I went crazy."

Dawa says he marched to the Lesbos municipality and demanded that space be found to bury the dead. Within a day, he says, the municipality had found a plot of land and allowed him to perform a Muslim burial, washing the dead and wrapping the bodies in burial shrouds.

"The first burial rites I did between two parked cars, for privacy, before I got a tent. Now, I have a tiled room with hot water on the property to do it properly."

Stemming the tide?

Hundreds of thousands fleeing Syria, Iraq, Afghanistan and other countries plagued by war and poverty have landed on Lesbos in the last year, the deadliest for migrants and refugees crossing the Mediterranean. Thousands have drowned or gone missing.

Photos: A man with his mouth sewn shut silently protests on the Greek-Macedonian border. Hide Caption 1 of 7 Photos: The 'Iranian' men are protesting the Macedonian government's decision to only allow Syrians, Iraqis and Afghans -- those fleeing war - to pass across the border. Hide Caption 2 of 7 Photos: Swedish Deputy Prime Minister Asa Romson fights tears as she announces Sweden's "open door" policy for asylum is ending. Hide Caption 3 of 7 Photos: A Macedonian police officer hits a man with his baton near Idomeni at the Greek-Macedonian border -- this is part of the so-called Balkans Route to northern Europe. Hide Caption 4 of 7 Photos: Refugees and migrants arrives on the Greek Island of Lesbos, after crossing the Aegean sea from Turkey. Hide Caption 5 of 7 Photos: As the first snows of the season fall in Germany, a sandalled refugee girl plays in front of a former army barracks now serving as a shelter for asylum seekers. Hide Caption 6 of 7 Photos: Migrants and refugees in the migrant camp known as the "Jungle" near the northern French port of Calais where some 4,500 people live. Hide Caption 7 of 7

The numbers of people crossing has dropped dramatically since the EU struck a deal with Turkey to deport most of those who reach Greece. Nonetheless, last week a boat capsized, killing four women and one child. Another four remain missing.

Marvahilis, the cemetery caretaker, is sure he and Dawa will still have work to do.

"We can send them one way but they'll just come back another," he says with a shrug.

"They'll still come, no matter what agreement is signed."