diff --git a/yt_dlp/__init__.py b/yt_dlp/__init__.py
index 81c970b72..4aa9dca8e 100644
--- a/yt_dlp/__init__.py
+++ b/yt_dlp/__init__.py
@@ -321,25 +321,12 @@ def validate_outtmpl(tmpl, msg):
         del opts.outtmpl['default']
 
     def parse_chapters(name, value):
-        def parse_timestamp(x):
-            # FIXME: Maybe there's a better way to remove parenthesis
-            x = x.replace('(', '').replace(')', '')
-
-            # FIXME: This should be smarter, e.g. 'inf-1day'?
-            if x in ('inf', 'infinite'):
-                return float('inf')
-
-            if re.match(r'[\d:]+', x):
-                return parse_duration(x)
-
-            return datetime_from_str(x, precision='second', use_utc=False).timestamp()
-
         chapters, ranges = [], []
+        parse_timestamp = lambda x: float('inf') if x in ('inf', 'infinite') else parse_duration(x)
         for regex in value or []:
             if regex.startswith('*'):
                 for range_ in map(str.strip, regex[1:].split(',')):
-                    # FIXME: This should match correctly '(now-1hour)-(now-20minutes)'
-                    mobj = range_ != '-' and re.fullmatch(r'(.+)?\s*-\s*(.+)?', range_)
+                    mobj = range_ != '-' and re.fullmatch(r'(-?[^-]+)?\s*-\s*(-?[^-]+)?', range_)
                     dur = mobj and (parse_timestamp(mobj.group(1) or '0'), parse_timestamp(mobj.group(2) or 'inf'))
                     if None in (dur or [None]):
                         raise ValueError(f'invalid {name} time range "{regex}". Must be of the form "*start-end"')
diff --git a/yt_dlp/extractor/youtube.py b/yt_dlp/extractor/youtube.py
index cc0b5401d..a0f93b2a8 100644
--- a/yt_dlp/extractor/youtube.py
+++ b/yt_dlp/extractor/youtube.py
@@ -2764,8 +2764,9 @@ def _live_dash_fragments(self, video_id, format_id, live_start_time, mpd_feed, m
 
         begin_index = 0
         download_start_time = ctx.get('start') or time.time()
-        section_start = ctx.get('section_start') or 0
-        section_end = ctx.get('section_end') or math.inf
+
+        section_start = 0 if ctx.get('section_start') is None else download_start_time + ctx['section_start']
+        section_end = math.inf if ctx.get('section_end') is None else download_start_time + ctx['section_end']
 
         lack_early_segments = download_start_time - (live_start_time or download_start_time) > MAX_DURATION
         if lack_early_segments:
diff --git a/yt_dlp/utils.py b/yt_dlp/utils.py
index ed7516967..07bc3f5a0 100644
--- a/yt_dlp/utils.py
+++ b/yt_dlp/utils.py
@@ -2667,16 +2667,19 @@ def parse_duration(s):
 
     days, hours, mins, secs, ms = [None] * 5
     m = re.match(r'''(?x)
+            (?P<sign>[+-])?
             (?P<before_secs>
                 (?:(?:(?P<days>[0-9]+):)?(?P<hours>[0-9]+):)?(?P<mins>[0-9]+):)?
             (?P<secs>(?(before_secs)[0-9]{1,2}|[0-9]+))
             (?P<ms>[.:][0-9]+)?Z?$
         ''', s)
     if m:
-        days, hours, mins, secs, ms = m.group('days', 'hours', 'mins', 'secs', 'ms')
+        sign, days, hours, mins, secs, ms = m.group('sign', 'days', 'hours', 'mins', 'secs', 'ms')
     else:
         m = re.match(
-            r'''(?ix)(?:P?
+            r'''(?ix)(?:
+                (?P<sign>[+-])?
+                P?
                 (?:
                     [0-9]+\s*y(?:ears?)?,?\s*
                 )?
@@ -2700,17 +2703,19 @@ def parse_duration(s):
                     (?P<secs>[0-9]+)(?P<ms>\.[0-9]+)?\s*s(?:ec(?:ond)?s?)?\s*
                 )?Z?$''', s)
         if m:
-            days, hours, mins, secs, ms = m.groups()
+            sign, days, hours, mins, secs, ms = m.groups()
         else:
-            m = re.match(r'(?i)(?:(?P<hours>[0-9.]+)\s*(?:hours?)|(?P<mins>[0-9.]+)\s*(?:mins?\.?|minutes?)\s*)Z?$', s)
+            m = re.match(r'(?i)(?P<sign>[+-])?(?:(?P<hours>[0-9.]+)\s*(?:hours?)|(?P<mins>[0-9.]+)\s*(?:mins?\.?|minutes?)\s*)Z?$', s)
             if m:
-                hours, mins = m.groups()
+                sign, hours, mins = m.groups()
             else:
                 return None
 
+    sign = -1 if sign == '-' else 1
+
     if ms:
         ms = ms.replace(':', '.')
-    return sum(float(part or 0) * mult for part, mult in (
+    return sign * sum(float(part or 0) * mult for part, mult in (
         (days, 86400), (hours, 3600), (mins, 60), (secs, 1), (ms, 1)))