Problem with meta box in Links

I have troubles saving the data of the meta box in the link part of the admin.
My code is working, because when I try it in the post or page part, it saves the data, but in Links it just won’t.

Here is my code. Should I write something else instead of ‘save_post’ ? I saw some used ‘save_link’ ans tried even though people replying said it didn’t exist, but it doesn’t work…
What I mean by that is that it works when I add it to post or page, but when I change ‘page’ (or ‘post’) to ‘link’ when I add the meta box, nothing is saved, and my input comes back blank when I go to the link form again, when I should have the link of my image. The data isn’t saved in the database either and I have no idea why.

Here is my code :

    add_action( 'admin_init', 'meta_boxes_setupa' );
function meta_boxes_setupa() {
    add_action( 'add_meta_boxes', 'mytheme_add_box' );
    add_action( 'save_post', 'mytheme_save_data', 10, 2 );
}
// add_action('admin_menu', 'mytheme_add_box');
// Add meta box
function mytheme_add_box() {
        add_meta_box(
                        'my-meta-box',
                        'Ajouter le logo de la société',
                        'mytheme_show_box',
                        'link',
                        'normal',
                        'high'
        );
}

// Callback function to show fields in meta box
function mytheme_show_box( $object, $box ) {
        // global $post;
        // echo '<input type="hidden" name="mytheme_meta_box_nonce" value="', wp_create_nonce(basename(__FILE__)), '" />';
        // $meta = get_post_meta($post->ID, '_upload_image', true);
        ?>
        <?php wp_nonce_field( basename( __FILE__ ), 'url_nonce' ); ?>
                <label for="upload_image">Sélectionner le logo : </label>
                <input type="text" name="upload_image" id="upload_image" value="<?php echo esc_attr( get_post_meta( $object->ID, '_upload_image', true ) ); ?>" size="40" readonly="readonly" />
                <input type="button" name="upload_image_button" id="upload_image_button" value="Parcourir" ?>
        <?php
}


// Save data from meta box
function mytheme_save_data($post_id, $post) {
        if ( !isset( $_POST['url_nonce'] ) || !wp_verify_nonce( $_POST['url_nonce'], basename( __FILE__ ) ) )
        return $post_id;

    $post_type = get_post_type_object( $post->post_type );
    /* Check if the current user has permission to edit the post. */
    if ( !current_user_can( $post_type->cap->edit_post, $post_id ) )
        return $post_id;

    /* Get the posted data and sanitize it for use as an HTML class. */
        $new_meta_value = ( isset( $_POST['upload_image'] ) ? sanitize_html_class( $_POST['upload_image'] ) : '' );
    /* Get the meta key. */
    $meta_key = '_upload_image';
    /* Get the meta value of the custom field key. */
    $meta_value = get_post_meta( $post_id, $meta_key, true );
    /* If a new meta value was added and there was no previous value, add it. */
    if ( $new_meta_value && '' == $meta_value )
        add_post_meta( $post_id, $meta_key, $new_meta_value, true );
    /* If the new meta value does not match the old value, update it. */
    elseif ( $new_meta_value && $new_meta_value != $meta_value )
       update_post_meta( $post_id, $meta_key, $new_meta_value );
    /* If there is no new meta value but an old value exists, delete it. */
    elseif ( '' == $new_meta_value && $meta_value )
        delete_post_meta( $post_id, $meta_key, $meta_value );
}

function my_admin_scripts() {
        wp_enqueue_script('media-upload');
        wp_enqueue_script('thickbox');
        wp_register_script('my-upload', get_bloginfo('template_url') . '/functions/my-script.js', array('jquery','media-upload','thickbox'));
        wp_enqueue_script('my-upload');
}
function my_admin_styles() {
        wp_enqueue_style('thickbox');
}
add_action('admin_print_scripts', 'my_admin_scripts');
add_action('admin_print_styles', 'my_admin_styles');

Thank you for your help !