import re


def normalize_email(email):
    """ Normalize an email address for comparison """
    if '@' not in email:
        return email
    # Trim off any +garbage
    email = re.sub(r'\+[^@]*@', '@', email)
    name, domain = email.split('@')
    # Remove all periods
    return name.replace('.', '').lower() + '@' + domain.lower()