Filas de grupo si tienen intervalos de tiempo superpuestos

WITH C1 AS (
SELECT *,
  CASE 
WHEN start_time <= MAX(IFnull(end_time,'9999-12-31 00:00:00.000')) OVER(
  partition by id
  ORDER BY start_time 
  ROWS BETWEEN UNBOUNDED PRECEDING AND 1 PRECEDING
  ) 
  THEN 0 
  ELSE 1 
END AS isstart
FROM activity
) 
SELECT ID,start_time,end_time,
   SUM(isstart) OVER(partition by id ORDER BY ID ROWS UNBOUNDED PRECEDING) AS DG 
FROM C1;

Esto debería funcionar para usted