function YOUR_MODULE_views_query_alter(&$view, &$query) {
  if ($view->name = 'YOUR_VIEW' && !empty($view->exposed_raw_input['YOUR_FIELD']) {
    $transliterated = transliteration_get($view->exposed_raw_input['YOUR_FIELD']);
    // Traverse through the 'where' part of the query.
    foreach ($query->where as &$condition_group) {
      foreach ($condition_group['conditions'] as &$condition) {
        // If this is the part of the query filtering on your field, change the
        // condition value to the transliterated string.
        if ($condition['field'] == 'YOUR FIELD') {
          $condition['value'] = $transliterated;
        }
      }
    }
  }
}