DOC: Address review comments

doc/HOWTO_RELEASE.rst

@@ -40,11 +40,14 @@ installers may be available for a subset of these versions (see below).
 * **Windows**
 
   We build 32- and 64-bit wheels on Windows. Windows 7, 8 and 10 are supported.
-  We build NumPy using the `mingw-w64 toolchain`_ on Appveyor.
+  We build NumPy using the `mingw-w64 toolchain`_, `cibuildwheels`_ and GitHub
+  actions.
+
+.. _cibuildwheels: https://cibuildwheel.readthedocs.io/en/stable/
 
 * **Linux**
 
-  We build and ship `manylinux1 <https://www.python.org/dev/peps/pep-0513>`_
+  We build and ship `manylinux2014 <https://www.python.org/dev/peps/pep-0513>`_
   wheels for NumPy.  Many Linux distributions include their own binary builds
   of NumPy.
 
@@ -178,8 +181,8 @@ Check deprecations
 ------------------
 Before :ref:`the release branch is made <branching>`, it should be checked that
 all deprecated code that should be removed is actually removed, and all new
-deprecations say in the docstring or deprecation warning at what version the
-code will be removed.
+deprecations say in the docstring or deprecation warning what version the code
+will be removed.
 
 Check the C API version number
 ------------------------------
@@ -236,10 +239,10 @@ Check that the release notes are up-to-date.
 Update the release notes with a Highlights section. Mention some of the
 following:
 
-  - major new features
-  - deprecated and removed features
-  - supported Python versions
-  - for SciPy, supported NumPy version(s)
-  - outlook for the near future
+- major new features
+- deprecated and removed features
+- supported Python versions
+- for SciPy, supported NumPy version(s)
+- outlook for the near future
 
 .. _towncrier: https://pypi.org/project/towncrier/

doc/RELEASE_WALKTHROUGH.rst

@@ -1,11 +1,10 @@
 This is a walkthrough of the NumPy 1.21.0 release on Linux, modified for
-building on azure and uploading to `anaconda.org`_. The commands can be
-copied into the command line, but be sure to replace 1.21.0 by the correct
-version. This should be read together with the
+building with GitHub Actions and cibuildwheels and uploading to the
+`anaconda.org staging repository for NumPy <https://anaconda.org/multibuild-wheels-staging/numpy>`_.
+The commands can be copied into the command line, but be sure to replace 1.21.0
+by the correct version. This should be read together with the
 :ref:`general release guide <prepare_release>`.
 
-.. _anaconda.org : https://anaconda.org
-
 Facility preparation
 ====================
 
@@ -124,7 +123,7 @@ Build wheels via cibuildwheel (preferred)
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 Tagging the build at the beginning of this process will trigger a wheel build
-via cibuildwheel and upload wheels and an sdist to the staging area. The CI run
+via cibuildwheel and upload wheels and an sdist to the staging repo. The CI run
 on github actions (for all x86-based and macOS arm64 wheels) takes about 1 1/4
 hours. The CI run on travis (for aarch64) takes less time.