PHP mail function ignoring additional headers - php

Question

I'm trying to send a mail using the php mail() function
but for some reason I don't get, additional headers are ignored.
This is my code:
$errors = '';
$myemail = 'my#email.com';
$myemail_bcc = 'my_bbc#email.com';
if(empty($_POST['nome']) || empty($_POST['email']))
{
$errors .= "Error: You must fill Name and Email fields";
}
$name = $_POST['nome'];
$email_address = $_POST['email'];
$telefono = $_POST['telefono'];
$message = $_POST['messaggio'];
if (!preg_match(
"/^[_a-z0-9-]+(\.[_a-z0-9-]+)*#[a-z0-9-]+(\.[a-z0-9-]+)*(\.[a-z]{2,3})$/i",
$email_address))
{
$errors .= "<br />Error: You must use a valid email address";
}
// spediamo la mail
if( empty($errors))
{
$to = $myemail;
$email_subject = "New Request from: $name";
$email_body = "User data:.\n\n";
$email_body .= "Nome: $name \nEmail: $email_address \nTelefono: $telefono \n";
$email_body .= "Messaggio: \n$message";
$headers = "From: John Smith <$myemail>\r\n";
$headers .= "Reply-To: $name <$email_address>\r\n";
$headers .= "Bcc: $myemail_bcc";
mail($to,$email_subject,$email_body,$headers);
}
I've tried to vary the way I declare headers without names, just with emails:
$headers = "From: $myemail \r\n";
$headers .= "Reply-To: $email_address\r\n";
$headers .= "Bcc: $myemail_bcc";
and even just on one line
$headers = "From: $myemail\r\nReply-To: $name <$email_address>\r\nBcc: $myemail_bcc";
But in no case the mail is sento to the Bcc address, and the "reply" function in client email does not use the Reply-to address.
where am I wrong?