diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index 95e4ddff9..620b4dd20 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -14,6 +14,7 @@
 
 from .. import basis_rotation as br
 from .. import scale_variations as sv
+from ..io.types import InversionMethod
 from . import Operator, QuadKerBase
 
 logger = logging.getLogger(__name__)
@@ -31,7 +32,7 @@ def build_ome(A, matching_order, a_s, backward_method):
         perturbation matching order
     a_s : float
         strong coupling, needed only for the exact inverse
-    backward_method : ["exact", "expanded" or ""]
+    backward_method : InversionMethod or None
         empty or method for inverting the matching condition (exact or expanded)
 
     Returns
@@ -49,7 +50,7 @@ def build_ome(A, matching_order, a_s, backward_method):
     # .end
     ome = np.eye(len(A[0]), dtype=np.complex_)
     A = np.ascontiguousarray(A)
-    if backward_method == "expanded":
+    if backward_method is InversionMethod.EXPANDED:
         # expended inverse
         if matching_order[0] >= 1:
             ome -= a_s * A[0]
@@ -66,7 +67,7 @@ def build_ome(A, matching_order, a_s, backward_method):
         if matching_order[0] >= 3:
             ome += a_s**3 * A[2]
         # need inverse exact ?  so add the missing pieces
-        if backward_method == "exact":
+        if backward_method is InversionMethod.EXACT:
             ome = np.linalg.inv(ome)
     return ome
 
@@ -114,7 +115,7 @@ def quad_ker(
         number of active flavor below threshold
     L : float
         :math:``\ln(\mu_F^2 / m_h^2)``
-    backward_method : ["exact", "expanded" or ""]
+    backward_method : InversionMethod or None
         empty or method for inverting the matching condition (exact or expanded)
     is_msbar: bool
         add the |MSbar| contribution
@@ -140,7 +141,7 @@ def quad_ker(
     )
     sx_ns = sx.copy()
     if order[0] == 3 and (
-        (backward_method != "" and ker_base.is_singlet)
+        (backward_method is not None and ker_base.is_singlet)
         or (mode0 == 100 and mode1 == 100)
     ):
         # At N3LO for A_qq singlet or backward you need to compute
@@ -240,7 +241,7 @@ class OperatorMatrixElement(Operator):
 
     def __init__(self, config, managers, nf, q2, is_backward, L, is_msbar):
         super().__init__(config, managers, nf, q2, None)
-        self.backward_method = config["backward_inversion"] if is_backward else ""
+        self.backward_method = config["backward_inversion"] if is_backward else None
         if is_backward:
             self.is_intrinsic = True
         else:
@@ -265,7 +266,7 @@ def labels(self):
             logger.warning("%s: skipping non-singlet sector", self.log_label)
         else:
             labels.append((200, 200))
-            if self.is_intrinsic or self.backward_method != "":
+            if self.is_intrinsic or self.backward_method is not None:
                 # intrinsic labels, which are not zero at NLO
                 labels.append((br.matching_hminus_pid, br.matching_hminus_pid))
                 # These contributions are always 0 for the moment
@@ -281,7 +282,7 @@ def labels(self):
                     (br.matching_hplus_pid, 100),
                 ]
             )
-            if self.is_intrinsic or self.backward_method != "":
+            if self.is_intrinsic or self.backward_method is not None:
                 labels.extend(
                     [
                         (21, br.matching_hplus_pid),
diff --git a/tests/eko/evolution_operator/test_matchin_condition.py b/tests/eko/evolution_operator/test_matching_condition.py
similarity index 100%
rename from tests/eko/evolution_operator/test_matchin_condition.py
rename to tests/eko/evolution_operator/test_matching_condition.py
diff --git a/tests/eko/evolution_operator/test_ome.py b/tests/eko/evolution_operator/test_ome.py
index 2c0fdf644..86b8cff83 100644
--- a/tests/eko/evolution_operator/test_ome.py
+++ b/tests/eko/evolution_operator/test_ome.py
@@ -41,7 +41,7 @@ def test_build_ome_as():
         aS = A_singlet((o, 0), N, sx_singlet, nf, L, is_msbar, sx_ns)
 
         for a in [aNS, aS]:
-            for method in ["", "expanded", "exact"]:
+            for method in [None, InversionMethod.EXPANDED, InversionMethod.EXACT]:
                 dim = len(a[0])
                 if o != 1:
                     assert len(a) == o
@@ -62,7 +62,7 @@ def test_build_ome_nlo():
     aNSi = A_non_singlet((1, 0), N, sx, nf, L)
     aSi = A_singlet((1, 0), N, sx, nf, L, is_msbar)
     for a in [aNSi, aSi]:
-        for method in ["", "expanded", "exact"]:
+        for method in [None, InversionMethod.EXPANDED, InversionMethod.EXACT]:
             dim = len(a[0])
             # hh
             assert a[0, -1, -1] != 0.0
@@ -197,7 +197,7 @@ def test_quad_ker(monkeypatch):
             is_log=True,
             logx=0.123,
             areas=np.zeros(3),
-            backward_method="expanded",
+            backward_method=InversionMethod.EXPANDED,
             a_s=0.0,
             nf=3,
             L=0.0,
@@ -234,7 +234,7 @@ def test_quad_ker(monkeypatch):
             is_log=True,
             logx=0.123,
             areas=np.zeros(3),
-            backward_method="exact",
+            backward_method=InversionMethod.EXACT,
             a_s=0.0,
             nf=3,
             L=0.0,
@@ -306,7 +306,7 @@ def test_quad_ker(monkeypatch):
 #         "debug_skip_non_singlet": False,
 #         "ev_op_max_order": 1,
 #         "ev_op_iterations": 1,
-#         "backward_inversion": "",
+#         "backward_inversion": None,
 #     }
 #     g = OperatorGrid.from_dict(
 #         theory_card,
@@ -327,7 +327,7 @@ def test_quad_ker(monkeypatch):
 #         order=theory_card["PTO"],
 #         L=0,
 #         nf=4,
-#         backward_method="",
+#         backward_method=None,
 #         is_msbar=False,
 #     )