Prepare sample data:
create table tab (id int, study_start_time int, study_end_time int); insert into tab select * from ( select 1234 as id, 168 as study_start_time, 256 as study_end_time union all select 2345, 175, 233 union all select 1234, 256, 300 union all select 1234, 300, 389 union all select 1234, 389, 439 union all select 1234, 439, 460 union all select 1234, 460, 480 union all select 2345, 400, 425 union all select 4567, 200, 225 union all select 4567, 250, 270 union all select 4567, 270, 289 union all select 4567, 300, 310 union all select 4567, 320, 340 union all select 4567, 360, 370 union all select 4567, 370, 390 ) t;
The way to "merge" the lines:

I may have complicated it too much, but the result is as expected :-). It is possible to simplify it in SQL Server 2005+ using CTE and still get "oneliner" or use a temporary table (most DBMSs) and do it in several lines.
select * from ( select m1.id, m1.study_start_time, m2.study_end_time from ( select t.id, t.study_start_time, t.study_end_time, t2.study_end_time as et, t3.study_start_time as st from tab t left join tab t2 on t2.id = t.id and t2.study_start_time = t.study_end_time left join tab t3 on t3.id = t.id and t3.study_end_time = t.study_start_time ) m1 join ( select m1.* from ( select t.id, t.study_start_time, t.study_end_time, t2.study_end_time as et, t3.study_start_time as st from tab t left join tab t2 on t2.id = t.id and t2.study_start_time = t.study_end_time left join tab t3 on t3.id = t.id and t3.study_end_time = t.study_start_time ) m1 where m1.et is null and m1.st is not null ) m2 on m1.id = m2.id and m2.study_end_time = ( select min(study_end_time) from ( select t.id, t.study_start_time, t.study_end_time, t2.study_end_time as et, t3.study_start_time as st from tab t left join tab t2 on t2.id = t.id and t2.study_start_time = t.study_end_time left join tab t3 on t3.id = t.id and t3.study_end_time = t.study_start_time ) m3 where m3.id = m1.id and m3.study_end_time >= m1.study_end_time and m3.et is null and m3.st is not null ) where m1.et is not null and m1.st is null union select id, study_start_time, study_end_time from ( select t.id, t.study_start_time, t.study_end_time, t2.study_end_time as et, t3.study_start_time as st from tab t left join tab t2 on t2.id = t.id and t2.study_start_time = t.study_end_time left join tab t3 on t3.id = t.id and t3.study_end_time = t.study_start_time ) m3 where m3.et is null and m3.st is null ) tab order by id, study_start_time;
Final result:
id study_start_time study_end_time ----------- ---------------- -------------- 1234 168 480 2345 175 233 2345 400 425 4567 200 225 4567 250 289 4567 300 310 4567 320 340 4567 360 390