diff --git a/.travis.yml b/.travis.yml
index 0b62b133c..073017a99 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -114,13 +114,7 @@ script: tox
 after_success:
   - |
     if [[ "$PYTEST_COVERAGE" = 1 ]]; then
-      set -e
-      # Add last TOXENV to $PATH.
-      PATH="$PWD/.tox/${TOXENV##*,}/bin:$PATH"
-      coverage combine
-      coverage xml
-      coverage report -m
-      bash <(curl -s https://codecov.io/bash) -Z -X gcov -X coveragepy -X search -X xcode -X gcovout -X fix -f coverage.xml -n $TOXENV-$TRAVIS_OS_NAME
+      env CODECOV_NAME="$TOXENV-$TRAVIS_OS_NAME" scripts/report-coverage.sh
     fi
 
 notifications:
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 72e4af732..b3515d5e0 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -4,8 +4,6 @@ trigger:
 
 variables:
   PYTEST_ADDOPTS: "--junitxml=build/test-results/$(tox.env).xml -vv"
-  COVERAGE_FILE: "$(Build.Repository.LocalPath)/.coverage"
-  COVERAGE_PROCESS_START: "$(Build.Repository.LocalPath)/.coveragerc"
   PYTEST_COVERAGE: '0'
 
 jobs:
@@ -55,8 +53,13 @@ jobs:
   - script: python -m pip install --upgrade pip && python -m pip install tox
     displayName: 'Install tox'
 
-  - script: |
-      call scripts/setup-coverage-vars.bat || goto :eof
+  - bash: |
+      if [[ "$PYTEST_COVERAGE" == "1" ]]; then
+        export _PYTEST_TOX_COVERAGE_RUN="coverage run -m"
+        export _PYTEST_TOX_EXTRA_DEP=coverage-enable-subprocess
+        export COVERAGE_FILE="$PWD/.coverage"
+        export COVERAGE_PROCESS_START="$PWD/.coveragerc"
+      fi
       python -m tox -e $(tox.env)
     displayName: 'Run tests'
 
@@ -66,9 +69,12 @@ jobs:
       testRunTitle: '$(tox.env)'
     condition: succeededOrFailed()
 
-  - script: call scripts\upload-coverage.bat
-    displayName: 'Report and upload coverage'
-    condition: eq(variables['PYTEST_COVERAGE'], '1')
+  - bash: |
+      if [[ "$PYTEST_COVERAGE" == 1 ]]; then
+        scripts/report-coverage.sh
+      fi
     env:
+      CODECOV_NAME: $(tox.env)
       CODECOV_TOKEN: $(CODECOV_TOKEN)
-      PYTEST_CODECOV_NAME: $(tox.env)
+    displayName: Report and upload coverage
+    condition: eq(variables['PYTEST_COVERAGE'], '1')
diff --git a/scripts/report-coverage.sh b/scripts/report-coverage.sh
new file mode 100755
index 000000000..755783d2a
--- /dev/null
+++ b/scripts/report-coverage.sh
@@ -0,0 +1,16 @@
+#!/usr/bin/env bash
+
+set -e
+set -x
+
+if [ -z "$TOXENV" ]; then
+  python -m pip install coverage
+else
+  # Add last TOXENV to $PATH.
+  PATH="$PWD/.tox/${TOXENV##*,}/bin:$PATH"
+fi
+
+python -m coverage combine
+python -m coverage xml
+python -m coverage report -m
+bash <(curl -s https://codecov.io/bash) -Z -X gcov -X coveragepy -X search -X xcode -X gcovout -X fix -f coverage.xml
diff --git a/scripts/setup-coverage-vars.bat b/scripts/setup-coverage-vars.bat
deleted file mode 100644
index 7a4a6d4de..000000000
--- a/scripts/setup-coverage-vars.bat
+++ /dev/null
@@ -1,7 +0,0 @@
-if "%PYTEST_COVERAGE%" == "1" (
-  set "_PYTEST_TOX_COVERAGE_RUN=coverage run -m"
-  set "_PYTEST_TOX_EXTRA_DEP=coverage-enable-subprocess"
-  echo Coverage vars configured, PYTEST_COVERAGE=%PYTEST_COVERAGE%
-) else (
-  echo Skipping coverage vars setup, PYTEST_COVERAGE=%PYTEST_COVERAGE%
-)
diff --git a/scripts/upload-coverage.bat b/scripts/upload-coverage.bat
deleted file mode 100644
index 08ed57791..000000000
--- a/scripts/upload-coverage.bat
+++ /dev/null
@@ -1,16 +0,0 @@
-REM script called by Azure to combine and upload coverage information to codecov
-if "%PYTEST_COVERAGE%" == "1" (
-    echo Prepare to upload coverage information
-    if defined CODECOV_TOKEN (
-        echo CODECOV_TOKEN defined
-    ) else (
-        echo CODECOV_TOKEN NOT defined
-    )
-    python -m pip install codecov
-    python -m coverage combine
-    python -m coverage xml
-    python -m coverage report -m
-    scripts\retry python -m codecov --required -X gcov pycov search -f coverage.xml --name %PYTEST_CODECOV_NAME%
-) else (
-    echo Skipping coverage upload, PYTEST_COVERAGE=%PYTEST_COVERAGE%
-)