You need to use nested meta queries https://make.wordpress.org/core/2014/10/20/update-on-query-improvements-in-4-1/
and your going to need to dynamically generate the meta query. As an example the cycle portion of it might look something like this
$meta_query = array('relation' => 'AND');
if ($cycle) {
$sub_query = array('relation' => 'OR');
$cycles = explode(',', $cycle);
foreach ($cycles as $cycle) {
$sub_query[] = array(
'key' => 'cycle',
'value' => '"'.$cycle.'"'
'compare' => 'LIKE'
);
} // end foreach cycle
$meta_query[] = $sub_query;
} // end if cycle
Please note that the above has not been tested and is meant only as an example.
A word of caution, too many LIKE and nested LIKE queries could time out the request.
