Drupal - How to pass data between operations of a single Batch?

Thanks David for your answer. But unfortunately $context['sandbox'] values were not retained through operations - they were retained through iterations of the same operation but not between operations.

Interestingly though, I found that $context['results'] values were retained between each operation. I did a simple test using the following module:

<?php 
function mytest_menu() {
  $items = array();
  $items['admin/content/mytest'] = array(
    'title' => 'mytest',
    'page callback' => 'drupal_get_form',
    'page arguments' => array('mytest_form'),
    'access arguments' => array('administer content'),
    'type' => MENU_NORMAL_ITEM,
  );
  return $items;
}

function mytest_form() {
  $form = array();

  $form['submit'] = array(
    '#type' => 'submit',
    '#value' => t('Submit'),
  );
  return $form;
}

function mytest_form_submit($form, $form_state) {
  $batch = array(
    'title' => t('Working ...'),
    'operations' => array(),
    'finished' => 'mytest_batch_finished',
    'init_message' => t('Starting ...'),
    'progress_message' => t('Processed @current out of @total.'),
    'error_message' => t('An error occurred during processing'),
    'progressive' => FALSE
  );
  $batch['operations'][] = array('mytest_initialize', array('test data')); 
  $batch['operations'][] = array('mytest_perform', array('different data')); 
  $batch['operations'][] = array('mytest_perform', array('different data')); 
  $batch['operations'][] = array('mytest_perform', array('different data')); 
  batch_set($batch);
  batch_process('admin/content/mytest');
}

function mytest_initialize($d, &$context) {
  dsm($d);
  $context['results']['test'] = 'inti val';
  $context['test']['test'] = 'init val';
}

function mytest_perform ($d, &$context) {
  dsm($context);
  $context['results']['test'] = uniqid();
  $context['test']['test'] = $context['results']['test'];
}

function mytest_batch_finished($success, $results, $operations) {
  dsm($results);
}

After the batch finished, I could see the dsm()'d messages. voilà: values were retained.

http://i.stack.imgur.com/tkAXx.png

It seems like only $context['results'] was given to the next operation. Arbitrary keys ($context['my own key'] for example) didn't work.

Hope someone will find this useful :)

PS: *previous not previos (screenshot).